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A fracture toughness study of a volcanic tuff rock

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Title:
A fracture toughness study of a volcanic tuff rock
Creator:
Lewis, Norman F
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English
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176 leaves : illustrations ; 28 cm

Subjects

Subjects / Keywords:
Fracture mechanics ( lcsh )
Volcanic ash, tuff, etc ( lcsh )
Fracture mechanics ( fast )
Volcanic ash, tuff, etc ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 144-149).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Civil Engineering.
Statement of Responsibility:
by Norman F. Lewis, Jr.

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Source Institution:
University of Colorado Denver
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Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
20873557 ( OCLC )
ocm20873557
Classification:
LD1190.E53 1989m .L48 ( lcc )

Full Text
A FRACHJRE TOUGHNESS STUDY OF A
VOLCANIC TUFF ROCK
by
Norman F. Lewis, Jr.
B.Sc. Colorado School of Mines, 1970
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Civil Engineering
1989


This thesis for the Master of Science degree by
Norman F. Lewis, Jr.
has been approved for the
Department of
Civil Engineering
by
Date
/?/ ,


Lewis, Norman F., Jr (M.Sc. Civil Engineering)
A Fracture Toughness Study of a Volcanic Tuff Rock
Thesis directed by Professor Nien-Yin Chang
Cores of a volcanic tuff from near Gunnison, Colorado,
have been tested for short rod fracture toughness.
The fracture toughness of a material is a measure of the
critical stress intensity factor at a crack tip under load. The
theoretical basis for fracture toughness lies in Griffith-Irwin
theory and linear elastic fracture mechanics. Theoretically, it
is a material property. The underlying theory was formulated for
metals but in recent years has been extended to other materials,
including rocks.
Using ISRM draft procedures for determination of fracture
toughness of rocks using core-based specimens, testing has been
performed on a suite of specimens. Specimens were divided into
three density groups of 40, 39 and 40 specimens each,
respectively. Each group was divided into eight groups of five
specimens each. Eight test paths were followed for the study.
Testing was done at roam temperature and after heating to 50, 100
and 200C, under dry and wet conditions.
Results of testing indicate that for the material tested,
fracture toughness increases with heating temperature up to 100C,
and then generally decreases with further increase in heating
temperature. This trend is evident for both dry and wet testing.
Fracture toughness appears to be highly dependant on density and


IV
moisture content. It increases with increasing density and
decreasing water content.
Limited Brazilian tensile strength data show similar
temperature, density, and moisture dependance as the fracture
toughness.
Test results indicate that fracture toughness probably
cannot be considered a material property for rock. However, it
can be used as an index property for rock classification and for
monitoring engineering projects. The test procedure does not
appear simple enough for rapid on-site testing.
The form and content of this abstract are approved. I recommend
its publication.


DEDICATION
This thesis is lovingly dedicated to my wife, Linda, and
my children, John, Laura, Nathan, Matthew, and Michael, who have
patiently endured while I have had to spend so much of my time
away from them preparing this thesis. Without their quiet
support, this work would not have been possible.


ACKNOWLEDGEMENTS
The author wishes to acknowledge the guidance, advice and
assistance received from numerous individuals during the
preparation of this thesis. Dr. Joseph F. labuz, formerly of the
University of Colorado at Denver and currently at the University
of Minnesota, was my adviser during the early phases of this
study. The idea for this study stems from discussions in his rock
mechanics classes at the University of Colorado. Dr. N.-Y. Chang
assumed the role of my adviser after Dr. Labuz left UCD. Drs.
Tzong H. Wu and Judith Stalnaker kindly sat as members of my
thesis committee, providing useful advice and suggestions during
the final stages of this study. Ned Larson of Jacobs Engineering
Albuquerque, New Mexico, provided the core used for this study.
Without the large quantity of core he was able to provide, the
study would not have been possible. Ken Criley of Chen-Northern
provided the vise of specialized laboratory equipment and
facilities for the preparation of test specimens and the
performance of tests. Dr. Brian Brady of the U.S. Bureau of Mines
provided the special holding fixture for cutting chevron notches
in the test specimens. Dr. N.-Y. Chang provided partial financial
assistance to pay for the manufacture of the test specimen grips.
Lastly, Nancy Anderson provided the much-needed word processing
expertise necessary to enable this thesis to became a reality.


CONTENTS
CHAPTER
I. INTRODUCTION
1.1 Purpose of the Study............................. 1
1.2 Scope of Study................................... 1
1.3 Background of the Study.......................... 3
1.4 Arrangement of the Thesis........................... 6
II. LITERATURE REVIEW
2.1 Introduction........................................ 7
2.2 Development of Theory............................... 7
2.3 Application of Theory to Rock Mechanics............. 8
III. THEORETICAL BACKGROUND
3.1 Introduction....................................... 14
3.2 Griffith-Irwin Theory.............................. 15
3.2.1 Griffith Hypothesis.............................. 15
3.2.2 Irwin Modifications.............................. 20
3.2.3 Other Modifications and Developments............. 23
3.2.4 Critical Appraisal of Approach................... 24
3.3 Linear Elastic Fracture Mechanics.................. 25
3.3.1 Introduction..................................... 25
3.3.2 Stress Intensity Factor.......................... 25
3.3.3 Crack Tip Zone................................... 29
3.3.3.1 Plastic Zone in Metals
29


Vlll
3.3.3.2 Micrx>-crac)dj'ig Zone in Rocks................ 30
3.4 Short Rod Specimen Testing........................ 34
3.4.1 Introduction and Background...................... 34
3.4.2 Theoretical Basis................................ 35
3.4.3 Critical Appraisal............................... 40
3.5 Application of Toughness Testing to Rock.......... 42
IV. TEST PROCEDURES
4.1 Purpose of Testing................................ 45
4.2 Test Specimens.................................... 46
4.2.1 Test Material.................................... 46
4.2.2 Specimen Preparation............................. 46
4.2.3 Petrographic Examination......................... 51
4.3 Test Procedures................................... 51
4.3.1 ISRM Level I Testing............................. 51
4.3.2 Heat Effects..................................... 51
4.3.3 Water Effects.................................... 55
4.4 Data Handling...................................... 55
4.4.1 Data File........................................ 55
4.4.2 Data Calculations................................ 56
4.5 Critique of Procedures............................. 58
4.5.1 Test Specimen Preparation Difficulties........... 58
4.5.2 Test Procedure Difficulties...................... 62
V. TEST RESULTS
5.1 Introduction....................................... 66
5.2 Fhysical Properties................................ 66
5.2.1 Petrographic Description......................... 66


IX
5.2.1.1 Source.......................................... 66
5.2.1.2 Macroscopic Features.......................... 68
5.2.1.3 Microscopic Features............................ 69
5.2.2 Standard Properties............................... 71
5.2.2.1 Density......................................... 71
5.2.2.2 Water Content................................... 72
5.2.3 Strength Properties............................... 72
5.2.3.1 Uniaxial Compressive Strength................... 72
5.2.3.2 Brazilian Tensile Strength...................... 76
5.3 Fracture Toughness................................ 78
5.3.1 Data Compilation.................................. 78
5.3.1.1 Data Tables................................... 78
5.3.1.2 Data Tests.................................... 78
5.3.1.3 Data Sorting.................................. 82
5.3.2 Group Besults..................................... 82
5.3.2.1 Group A......................................... 82
5.3.2.2 Group B......................................... 88
5.3.2.3 Group C......................................... 88
5.3.2.4 Composites...................................... 88
VI. DISCUSSION OF TEST RESULTS
6.1 Introduction....................................... 103
6.2 Physical Properties................................ 103
6.2.1 Composition...................................... 103
6.2.2 Standard Properties.............................. 104
6.2.3 Strength Properties.............................. 106
6.3 Fracture Toughness............................... 107


X
6.3.1 Out-of-Plane Breaks............................. 107
6.3.2 Trends and Comparisons Within Groups............ 107
6.3.2.1 Group A...................................... 107
6.3.2.2 Group B...................................... 118
6.3.2.3 Group C...................................... 120
6.3.3 Trends and Comparisons Among Groups........... 123
6.3.3.1 Density...................................... 123
6.3.3.2 Temperature.................................. 128
6.3.3.3 Comparison With Other Studies................ 131
6.4 Validity of Test Results.......................... 132
VII. CONCLUSIONS
7.1 Results of Study................................... 136
7.1.1 Effects of Composition......................... 136
7.1.2 Effects of Density............................. 137
7.1.3 Effects of Heat................................ 137
7.1.4 Effects of Moisture............................ 138
7.1.5 Interrelations of Effects....................... 138
7.1.6 Usefulness of Test Method....................... 139
7.2 Comparison to Previous Studies.................... 140
7.2.1 Standard Property Testing....................... 140
7.2.2 Fracture Toughness Testing...................... 140
7.3 Application of Results............................ 140
7.3.1 Test Methods.................................... 140
7.3.2 Rock Classification............................. 141
7.3.3 Index Property.................................. 141
7.3.4 Material Property............................... 141


XI
7.4 Recommendations for Further Study................ 142
7.4.1 General......................................... 142
7.4.2 Testing at Elevated Temperatures............... 142
7.4.3 Testing at Different Moisture Contents......... 142
7.4.4 Level II ISRM Testing........................... 142
7.4.5 Other Rock Types............................... 143
BIBLIOGRAPHY.................................................. 144
APPENDIX...................................................... 150


TABLES
Table
1. Summary of thin-section petrographic examination......... 70
2. Moisture determinations.................................. 73
3. Tuff strength data....................................... 74
4. Brazilian tensile strength data.......................... 77
5. Fracture toughness test data (Group A)................... 79
6. Fracture toughness test data (Group B)................... 80
7. Fracture toughness test data (Group C)................... 81
8. Group A fracture toughness data summary.................. 83
9. Group B fracture toughness data summary.................. 89
10. Group C fracture toughness data summary.................. 94
11. Fracture toughness (mean values)....................... 121
12. Evaluation of fracture toughness results at 25C,
according to Barker (1984) criterion.................. 135


FIGURES
Figure
1. Elliptic hole in a plate.............................. 17
2. Relations at crack tip (Schmidt, 1980).............. 22
3. Three basic inodes of deformation (Schmidt and
Rossmanith, 1983)..................................... 27
4. Shape of plastic zone with Von Mises yield criterion
(Schmidt, 1980).......................................... 31
5. Shape of microcracking zone with maximum normal stress
yield criterion (Schmidt, 1980).......................... 33
6. Short rod specimen configuration (Barker, 1977b)......... 36
7. Load application for short rod specimen (Barker, 1977b) 37
8. Nomenclature for theoretical analysis of short rod
specimen (Barker, 1977a)................................. 38
9. Stress intensity minimum versus crack opening
resistance (Newman, 1984)................................ 43
10. Set-up for grinding ends of short rod specimens.......... 48
11. Set-up for cutting notch in short rod specimens.......... 49
12. Close-up of notch cutting device......................... 50
13. Procedure for attaching end plates to short rod
specimens................................................ 52
14. Apparatus for Level I short rod fracture toughness
tests.................................................... 54
15. Fracture toughness test grips............................ 63
16. Close-15) view of fracture toughness test grips with
specimen in place........................................ 64
17. Source location of tuff used for study................. 67
18. Rock deformation collars for determination of Young's
modulus and Poisson's ratio.............................. 75


xiv
19. Group A: Plot of fracture toughness versus density at
25C.................................................. 84
20. Group A: Plot of fracture toughness versus density at
50 C................................................. 85
21. Group A: Plot of fracture toughness versus density at
100C................................................. 86
22. Group A: Plot of fracture toughness versus density at
200 C................................................ 87
23. Group B: Plot of fracture toughness versus density at
25C..................................................... 90
24. Group B: Plot of fracture toughness versus density at
50 C.................................................... 91
25. Group B: Plot of fracutre toughness versus density at
100C.................................................... 92
26. Group B: Plot of fracture toughness versus density at
200C.................................................... 93
27. Group C: Plot of fracture toughness versus density at
25C..................................................... 95
28. Group C: Plot of fracture toughness versus density at
50 C.................................................... 96
29. Group C: Plot of fracture toughness versus density at
100C.................................................... 97
30. Group C: Plot of fracture toughness versus density at
200 C................................................... 98
31. Groups A,B,C: Composite plot of fracture toughness
versus density at 25 C.................................. 99
32. Groups A,B,C: Composite plot of fracture toughness
versus density at 50 C................................. 100
33. Groups A,B,C: Composite plot of fracture toughness
versus density at 100 C................................ 101
34. Groups A,B,C: Composite plot of fracture toughness
versus density at 200 C................................ 102
35. Drill hole density intervals and group intervals......... 105
36. Normal break, specimen A-3.............................. 108


XV
37. Normal break, specimen B-16............................ 109
38. Normal initial break with slight migration out of
plane after peak load, specimen 017.................... 110
39. Break with migration out of plane in one ligament
after peak load, specimen 08........................... Ill
40. Break with migration out of plane in both ligaments
after peak load, specimen A-ll......................... 112
41. Invalid test break; migration out of plane before peak
load, specimen A-15.................................... 113
42. Group A; Mean fracture toughness versus test
temperature............................................ 115
43. Grot?) A: Brazilian tensile strength versus fracture
toughness at 25C, dry................................. 117
44. Group B: Mean fracture toughness versus test
tenperature............................................ 119
45. Group C: Mean fracture toughness versus test
temperature............................................ 122
46. Groups A,B,C: Composite plot of fracture toughness
versus density at 25C, with linear regression
lines for dry and wet groups........................... 124
47. Groups A,B,C: Composite plot of fracture toughness
versus density at 50C, with linear regression
lines for dry and wet groups........................... 125
48. Groups A,B,C: Composite plot of fracture toughness
versus density at 100C, with linear regression
lines for dry and wet groups........................... 126
49. Groups A,B,C: Composite plot of fracture toughness
versus density at 200C, with linear regression
lines for dry and wet groups........................... 127
50. Groups A,B,C: Mean fracture toughness versus test
temperature, dry....................................... 129
51. Groups A,B,C: Mean fracture toughness versus test
temperature, wet
130


CHAPTER I
INTRODUCTION
1.1 Purpose of the Study
The purpose of this study was to test a volcanic tuff rock
for its plane strain fracture toughness under various conditions.
Results of the testing would be used to evaluate the validity and
usefulness of the parameter as a material property and as an index
property to aid in excavation planning for an underground nuclear
waste repository and other engineering projects in volcanic tuff
units. Along with the evaluation, an analysis of how fracture
toughness changes with density, thermal effects, and the presence
of water would be developed. Suitable conclusions were to be
drawn where appropriate.
Draft test procedures of the International Society for
Rock Mechanics (ISRM, 1986), for the determination of plane strain
fracture toughness of rock were to be followed for testing. In
addition, the procedures were to be evaluated for their ease or
difficulty of performance by a typical geotechnical laboratory.
Subsequent to completing most of the testing for this study, the
draft procedures were published by the ISRM as "suggested methods"
(ISRM, 1988). There appears to be no significant difference


2
between the draft procedures used for this study and the recently
published "suggested methods".
1.2 Scope of Study
The study is centered on the testing of a volcanic tuff in
the form of NX wireline core (dia. = 1.87") for its plane strain
fracture toughness. Testing has been done using the short rod
configuration according to the ISEM draft testing guidelines
(ISEM, 1986) A suitable tuff from the Gunnison, Colorado, area
was chosen for its availability in guantity in core form and for
its possible similarity to the Yucca Mountain, Nuclear Test Site,
Nevada, tuffs, which are under consideration as a high level
nuclear waste repository.
From the available core, three density groups of specimens
were assembled, with each group containing 40 specimens. This
provided five samples for each of eight test paths. Specimens
were tested in the dry state at room temperature (25C ) and
after heating to 50C, 100C, or 200C for 24 hours. Additional
samples were then tested after heating to the same temperatures
and then immersing in water for 24 hours prior to testing. Peak
fracture load was recorded for all tests and the plane strain
fracture toughness was calculated.
Fracture toughness was determined according to Level I
testing of the ISEM guidelines. Calculated values may vary from
the true fracture toughness value to some degree due to plasticity
effects, but the calculated values were deemed adequate to study


3
the relative changes due to density, temperature, and moisture
effects.
Petrographic studies were made of representative
specimens. At least one specimen from each core hole represented
in a density group was examined for its constituents and texture.
Special attention was made to any possible textural anisotropies
in hand and thin-section examinations.
Specimens from each density group were tested for their
Brazilian tensile strength at 25C. One group was tested after
heating to 100 C. At least four to five specimens from each
density group were tested at each temperature.
Data were evaluated to determine the effects of the
various test conditions on the fracture toughness of the rock.
Suitable conclusions were made where appropriate. Observations
made during specimen preparation and testing were combined with
test results to assess the validity and usefulness of the test
procedures and the resultant fracture toughness values.
1.3 Background of the Study
Rock fracture toughness is a property that has been
finding increased use in the study of rock fracture. The concept
of fracture toughness was originally applied to metals but the
same principles have been extended, with certain modifications, to
the analysis of rock fracture. For metals, fracture toughness is
considered to be a material property and finds wide application in
the study of sub-critical failure of metals. For rock, fracture


4
toughness has not yet gained acceptance as a material property,
although some studies indicate that it may be so on at least a
limited basis. As an index property, however, fracture toughness
may find wide application in studies of rock fracture and failure
related to engineering projects.
The theoretical basis for fracture toughness testing lies
in Griffith-Irwin theory and linear elastic fracture mechanics.
The plane strain fracture toughness, Kjc, by theory, is a material
property. However, with rock, numerous factors are present that
can affect and limit the theoretical application and thus prevent
Klc from being a true material property.
The ISKM is presently studying a proposed test procedure
for the determination of plane strain fracture toughness for rock
cores. Testing is based on two specimen geometries, the chevron-
notched bar and the chevron-notched short rod. Since core is a
commonly available sample configuration in engineering projects, a
test procedure for fracture toughness based upon core may prove
useful and convenient.
In the past 10 to 15 years, numerous studies have been
published concerning the determination of rock fracture toughness.
Most have used specimens prepared according to metals testing
guidelines and thus extensive specimen preparation has been
required, most of which is not practical for engineering studies
unless large blocks of rock and elaborate machining facilities are
available. Because of this, there has been increased interest in
methods that utilize core for testing. Core specimens cannot


5
strictly meet the same test criteria applied to metals testing,
but sufficient evidence has been coming forth to indicate a
reasonable validity to core-based testing.
Fracture of rock is influenced by numerous factors, heat
and water probably being the most significant, given a reasonably
uniform rock type. Elevated temperatures tend to lower rock
fracture energies due to thermal cracking. As rock heats, it
expands, causing stresses to develop that lead to or facilitate
fracture initiation. Water contributes to stress corrosion,
generally causing an acceleration of fracture rates and thus an
overall lowering of fracture energies. The effects of either
temperature or water, or both combined, are, in turn, influenced
by the constituent mineralogy and texture of the rock mass.
Tuffaceous rocks of the Nuclear Test Site (NTS) in
southeastern Nevada are currently the only rocks remaining under
serious consideration as a site for a high-level nuclear waste
repository. Studies of the fracture toughness of such rocks and
how it varies according to intrinsic and environmental factors can
be of use in evaluating the suitability of such rocks for
repository siting, as well as evaluating mining requirements.
For this study, a rhyolite tuff considered to be similar
to the tuff units at Yucca Mountain, NTS, was chosen to determine
its plane strain fracture toughness (Kjc) and to study how that
value may be affected by heat and/or water. A third variable,
density, has also been introduced in the evaluation, as tuff units
tend to have widely varying densities. Testing has been done


6
according to ISKM draft guidelines for the chevron-notched short
rod test configuration, with Level I testing used throughout.
Fracture toughness values obtained in Level I testing do not
necessarily represent the "true" value but were deemed adequate
for the purposes of this study. Numerous other published fracture
toughness studies probably did not obtain a "true" toughness value
either, although that has not always been stated.
Prior to presentation of the test methods and results, a
thorough review of the literature as well as a comprehensive
review of the theory behind fracture toughness testing are
presented.
1.4 Arrangement of the Thesis
The thesis is so arranged as to guide the reader through
an outline of fracture toughness testing and its potential
usefulness, followed by an extensive review of the literature. A
discussion of the theory behind the testing follows. With this
background, the reader can more readily understand and critique
the test procedures and results of the study.
Experimental procedures are covered in detail and are
followed by a presentation of the experimental results. Content
of these sections is evaluated in a discussion of the test
results. Finally, major conclusions which may be reasonably made
from the study are discussed. Suggestions are made for additional
study.


CHAPTER II
UTERATURE REVIEW
2.1 Introduction
Rock fracture mechanics is a rather recent field of study
(Schmidt and Rossmanith, 1983). Fracture mechanics should not be
confused with failure mechanics. Failure mechanics refers to the
overall process in which a rock or rock mass sustains permanent
damage and has been studied extensively. Fracture mechanics,
however, refers to the study of discrete crack propagation which
may or may not result in failure of the rock or rock mass.
Fracture mechanics, or more properly, linear elastic
fracture mechanics (IEFM), has evolved over the past 30-plus years
as engineers sought to understand the brittle failure of
structures made of high strength metal alloys (Schmidt and
Rossmanith, 1983). Instances of catastrophic metal failures well
belcw the yield strength during World War II had pointed out the
great need of a theoretical basis for understanding the failures.
2.2 Development of Theory
Present fracture mechanics theory had its beginnings with
the studies of A.A. Griffith (1921, 1924). He studied the
propagation of cracks in thin glass plates and developed a


8
relation between the strain energy release rate of a migrating
crack and the potential energy stored in the crack. His studies
gained little acceptance until after World War II when Irwin and
Orowan published papers discussing fracturing in metals and its
relation to Griffith's theory (Orowan, 1952; Irwin and Kies,
1952). In 1957, Irwin proposed modifications to Griffith's theory
that became the basis for present-day linear elastic fracture
mechanics (IEFM). Basically, his modified theory stated that at
the onset of unstable fracturing, the fracture work per unit crack
extension could be equated to the rate of disappearance of strain
energy from the surrounding elastically strained material (Irwin,
1957). From this came the concept of a stress intensity factor
which could be evaluated in order to study the fracture process.
Development of IEFM principles for metals was rapid and
culminated in the adoption of ASM E399, Standard Test Method for
Plane-Strain Fracture Toughness of Metallic Materials, in 1972.
The strong interest in fracture mechanics of metals is further
evidenced by annual ASTM symposia on fracture mechanics.
2.3 Application of Theory to Rock Mechanics
Application of fracture mechanics principles to rock
mechanics has generally been slew. Jaeger (1956) discussed
elasticity and its relation to rock properties and failure but he
did not discuss to any great extent the actual fracture initiation
process. Bieniawski (1967) discussed in detail failure and
fracture and made a distinction between various conditions and


9
stages of fracture. Bieniawski (1967) relied on the Griffith
theory as a criterion for fracture initiation and failure but his
studies were more concerned with rock failure rather than with
fracture initiation.
Bieniawski's studies were somewhat typical of the research
interests in rock mechanics at the time. Much emphasis was being
given to attempts to develop adequate failure criteria for rock
and rock masses. Eventually, however, it was through this type of
research that the importance of fracture initiation to the overall
failure process was being recognized. Also, it was becoming
increasingly necessary to be able to predict, and, if possible,
control the fracture process in rock for such situations as
hydraulic fracturing and blasting. A knowledge of fracture
processes was therefore necessary.
During the 1970's researchers attempted to apply the test
methods of ASTM E399 to rock, in order to try to quantify material
parameters involved in fracture initiation. One of the earliest
of such studies was that of Schmidt (1976) in which he used
several sizes of three-point-bend fracture specimens of Indiana
limestone to evaluate fracture toughness according to ASTM E399
standards. Using similar methods, Schmidt and Huddle (1977)
studied the effect of confining pressure on the fracture toughness
of Indiana limestone. Ingraffea and Schmidt (1978) used ASTM
procedures for an experimental verification of a fracture
mechanics model for the tensile strength prediction of Indiana
limestone. In 1977, an ASTM sub-committee on the Fracture Testing


10
of Brittle Non-Metallic Materials was formed, but as yet no
standard methods of testing have been adopted.
Since the late 1970's there has been a many-fold increase
in the number of papers published dealing with rock fracture
resistance studies, reflecting the vast increase in rock fracture
mechanics research. While much of this research has been aimed
toward evaluating plane strain fracture toughness (Klc) values,
much effort has also been devoted to R-curve and J-integral
approaches to fracture resistance evaluation. Ouchterlony (1980)
summarized much of the fracture toughness and J-integral research
to date and commented on the applicability of the approaches.
Schmidt and Rossmanith (1983) discussed the overall field of rock
fracture mechanics, focusing on fracture toughness testing.
Attention has moved away from using elaborately machined
ASTM E399-type rock specimens for testing to more practical types
of rock specimens. Most often, rock is available as core. Barker
(1977a,b) introduced the short rod specimen for fracture toughness
testing. This specimen geometry is ideal for rock core as less
material and sample preparation is required to produce a test
specimen. Extensive research (Barker, 1977b) has gone into the
theory of the short rod specimen as well as calibration and
verification of test results (Beech and Ingraffea, 1982; Bubsey,
Munz, Pierce, and Shannon, 1982). Newman (1984) presented a
thorough review of chevron-notched fracture specimens, including
the short rod specimen. Although Barker originally developed the
short rod test speciman for metals testing, seme of his initial


11
work was with rock. Ouchterlony and Ingraffea have been refining
the theory and procedures for the short rod specimen as well as
the three-point bar-in-bending specimen in order to allow the use
of commonly available rock core for comprehensive fracture
toughness and resistance testing.
From fracture mechanics research, fracture toughness has
emerged as a useful, but not necessarily material, property of
rock. Some researchers appear to accept it as a material
property, especially if rigorous test procedures are followed,
while others will only accept it as an index property. As an
index property, it may actually be more useful than such
traditional testing methods as point-load strength, Brazilian
tensile strength, and even unconfined compressive strength,
because it appears to exhibit less variability than the other
index properties (Gunsallus and Kulhawy, 1984). Nelson, et al.
(1985) considered fracture toughness to be a material property and
used it in an evaluation of tunnel boring machine performance (see
also Ingraffea, et al., 1982.
Rock fracture toughness research has generally focused on
extensional or Mode I-type loading, hence the designation Kjc for
most rock fracture toughness values. If one is studying rock
fracture in which extension (tension) is the dominant feature,
then the Klc values are appropriate. However, as pointed out by
Rudnicki (1980), to study geologic processes in the Earth's crust,
an understanding of shear, or Mode II, conditions is necessary.
It has not been possible to find published results for research


12
into Mode II fracture toughness. If, however, macroscopic shear
failure results from the link-up of micro-scale fractures, then
studies of KIc are likely to improve the understanding of
inelastic processes and fracture in rocks (Rudnicki, 1980).
The ISRM is presently studying draft procedures for core-
based testing of Mode I fracture toughness of rock. The proposed
procedures are based largely on the research of Ouchterlony and
Ingraffea and involve two specimen geometries, the short rod and
the three-point bar-in-bending (both chevron notched). If these
procedures are adapted, they may extend the usefulness of fracture
toughness data to the project engineer.
Environmental factors, namely heat and/or water, may have
a profound effect on fracture toughness. Heat induces thermal
cracking, thus potentially lowering fracture toughness. Water
facilitates stress-corrosion cracking, again potentially lowering
the fracture toughness of a rock. A few studies have made at
least an attempt to quantify the effects of heat and/or water.
Numerous studies have focused on the effect of heat on the
formation and propagation of microcracks, with no concern for
measuring fracture toughness or other parameters (Bauer and
Johnson, 1979). Fewer papers have discussed the role of water and
stress corrosion cracking. It appears that there have not, as
yet, been any research results published for a comprehensive study
of rock fracture toughness and how it may change due to heat
and/or stress corrosion cracking. As models of rock fracture
propagation are refined, such a knowledge will be necessary to


13
adequately model rock behavior under realistic geologic
conditions.


CHAPTER III
THEORETICAL BACKGROUND
3.1 Introduction
Over the past 30 to 40 years, fracture toughness testing
has become an established and useful tool in fracture mechanics
studies of metals. Testing seeks to establish a material
property, fracture toughness (K), which has a sound theoretical
basis and which is useful for predicting metal behavior. The
theory applies well to metals because of their generally good
linear-elastic behavior.
Application of fracture mechanics theory to rocks has been
slower and fraught with difficulties. However, over the last 10
years or so there has been a many-fold increase in research into
the application of fracture mechanics theory to rock, especially
as increased demands for fossil fuels, metals and geothermal
energy have necessitated greater efficiency in rock-fracturing
processes.
For most engineering disciplines the study of fracture
mechanics is intended to predict and prevent catastrophic failure.
However, in rock mechanics, cracking (failure) is considered to be
beneficial.


15
Fracture mechanics theory steins largely from the early
work of A.A. Griffith (1921) but did not really gain serious
attention until World War II. Since then, development of theory
has been rapid.
3.2 Griffith-Irwin Theory
3.2.1 Griffith Hypothesis
Griffith (1921) discussed rupture of solids and the
affects of "flaws" or cracks within an elastic body under stress.
He formulated a theoretical criterion of rupture, which, simply
stated is:
.. .the equilibrium state of an elastic solid body, deformed by
specified surface forces is such that the potential energy of
the whole system is a minimum. Ihe new criterion of rupture
is obtained by adding to this theorem the statement that the
equilibrium position, if equilibrium is possible, must be one
in which rupture of the solid has occurred, if the system can
pass from the unbroken to the broken condition by a process
involving a continuous decrease in potential energy.
(Griffith, 1921)
He further stated,
In an elastic solid body deformed by specific forces
applied at its surface, the sum of the potential energy of the
applied forces and the strain energy of the body is diminished
or unaltered by the introduction of a crack whose surfaces are
traction-free. (Griffith, 1921)
Applying Hooke's law, if an elastic body is deformed frcm
the unstrained state to a new equilibrium state by constant
forces, the potential energy of the new state is decreased by an
amount equal to twice the strain energy. Ihe net reduction in
potential energy is equal to the strain energy and thus the total
decrease in potential energy due to the formation of the crack is


16
equal to the increase in strain energy less the increase in
surface energy (Griffith, 1921).
Considering the case of a flat homogeneous isotropic plate
of uniform thickness which contains a slight crack passing
normally through it, if the plate is subjected to stresses applied
to the outer edges, the changes in energy can be quantified using
the following derivation, which Griffith based on a solution by
C.E. Inglis (1913) (Griffith, 1921, 1924).
Referring to Fig. 1, the crack is represented by an
elliptic hole, with its major axis, 2a, and its minor axis, 2b,
oriented with the cartesian coordinates x and y. The major axis
is large compared to the minor axis, giving the ellipse an
elongate, or flattened, aspect parallel to the x-axis. The
cartesian coordinates, x and y, are related to elliptic
coordinates a and /3 by:
x + iy = c cosh (a + i/3);
where a = constant and /3 = constant define two systems of curves
(ellipse and hyperbola) intersecting at right angles. The edge,
or surface, of the crack (ellipse) is given by a, while fH
specifies the positions of points on the ellipse. A state of
uniform stress exists far from the crack and is specified by three
principal tensions, P, Q, and R. P is normal to the plate; Q and
R are parallel to x and y, respectively, with R positive.
From an evaluation of particular cases, the strain energy
of the material within the ellipse, a, per unit thickness of plate
can be determined, as presented in the following cases.


17
R
y
Q
b

l
Ptnormal to x-y plant)
X
Q
' T t t 1'
R
Fig
1
Elliptic hole in a plate


Case A: Q = R, P = 0
The strain energy equals:
18
.5
f2n
Jo
(Uo/h)Raa d/3 +
.5
F27T
Jo
(u^/hJS^ d0
Where is the tensile stress normal to a = constant, is the
displacement normal to a = constant, is the displacement normal
to /3 = constant and is the shear stress in the directions of
the normals to a and (3. The modulus of transformation, h, of the
coordinates is given by:
{2/[c2 (cosh 2a cos 2(3)])1'2
where c is the half length of the focal line.
As a becomes large, the strain energy tends toward the
value:
(tf^R2 / 8/i)[(.5(p l)e2a) + ((p + l)cosh 2a0) ]
where ^ is the modulus of rigidity of the material, and
p = 3 4v for plane strain
p = (3 v) / (1 + v) for plane stress
(v is Poisson's ratio).
The boundary of the crack is given by a = a0. Therefore W, the
increase in strain energy due to the crack is:
W = (7TC2 R2 / 8/x) (p + 1) cosh 2a0
If a0 = 0, then W = (p + ljTrtfR2 / 8/1/
for a very narrow crack of length 2c.
Case B: R = 0, a0 = 0
W is found to be zero.


19
Case C; Q = R = 0, a0 = 0
The stresses are unaltered, so W = 0. Therefore, in a
general form, the increase in strain energy is given by:
W = (p + 1) 7TC2 R2 / 8jx
and W is determined entirely by R. The potential energy of the
surface of the crack is given by U = 4cT, where T is the surface
tension of the material.
The reduction of the potential energy of the system due
to the presence of the crack is:
W U = ((p + lJn-tfR2 / 8m) 4c?r
For the crack to extend,
i-(W U) = 0 or (p + l)7rcR2 = 16/iT
6c
The breaking stress is then:
R = (2E(1 v2 )T/ttc) ^, for plane strain conditions,
and
R = (2ET / ttc)1"2, for plane stress conditions,
where E is the Young's modulus of the material.
The chief difficulties with this derivation are accurate
values for the material properties, particularly the surface
tension, T.
Griffith attempted to verify the theory through a series
of experiments with glass in the form of cracked spherical bulbs
and cracked circular tubes. Essentially, his experiments shewed a
greater than ten-fold decrease in the maximum tension in the glass
at rupture as compared with the theoretical strength.


20
Griffith's general conclusion was that the observed
weakness of isotropic solids, as compared to their theoretical
strength, is due to the presence of discontinuities or "flaws.
If the flaws could be eliminated, effective strength would
approach theoretical strength. This was verified somewhat by
testing thin glass fibers.
According to Griffith's analysis, the actual tensile
strength of a material is related more to the force required to
extend the flaws than to a theoretical strength. The energy
balance between the surface energy of a crack, the strain energy
associated with it, and the work done by external forces
determines whether or not a crack will grow, leading to failure of
the material. The theoretical condition for failure has the form:
R = me-*, where m is a constant of the materials (Griffith, 1924).
3.2.2 Irwin Modifications
Griffith's theory found little application until the mid-
forties. In 1944, Zener and Hollcman first made a connection
between the brittle failure of metallic materials and Griffith
theory (Weiss and Yukawa, 1964). Qrowan and Irwin both found
evidence of extensive plastic deformation in materials that had
broken in a "brittle" fashion. In 1948, Irwin pointed out that
the work done in plastic deformation must be included in the
Griffith energy balance, and may actually be much more significant
than the work done against surface tension in the crack (Weiss and
Yukawa, 1964). Orowan independently reached the same conclusions.


21
In 1957, Irwin showed that the Griffith energy approach is
equivalent to a stress-intensity approach according to which
fracture occurs when a critical stress distribution,
characteristic of the material, is reached (Weiss and Yukawa,
1964).
The basic modified Griffith theory, as postulated by
Irwin, is that at the onset of unstable fast fracturing, the
fracture work per unit crack extension can be equated to the rate
of disappearance of strain energy from the surrounding
elastically-strained material (Irwin, 1957). Irwin was dealing
with conditions near the leading edge of a "somewhat brittle"
crack, indicating that large plastic deformations could be present
close to the crack, but they did not extend away from the crack
for more than a small fraction of the crack length.
Irwin defined a term, G, which is the strain energy loss
rate associated with extension of the fracture, accompanied only
by plastic strains local to the crack surfaces (Irwin, 1957). It
is the force component most directly related to crack extension
and thus the most useful. Using a Westergaard analysis for
stresses associated with a crack, Irwin determined that if a
relationship is established according to Fig. 2 (Irwin, 1957), the
stresses are given by:
Oy = [(EG / tt)1^] [cos(0/2) / (2r)^][l + sin(9/2) sin(30/2) ]
and
ctx = [(EG / 7r)^] [cos(0/2) / (2r)35] [1 sin(0/2) sin(30/2)]


22
Fig. 2. Relations at crack tip (Schmidt, 1980)


23
so long as r/a and r/(a b) approximate unity. G is independent
of r and 6, and is the magnitude of the energy transfer from
mechanical or strain energy into other forms of energy in the
vicinity of the crack. It may be regarded as the force tending to
cause crack extension.
. . . . 1,
The intensity factor is given as (EG/7T) 2, for plane stress
conditions, and can be measured by appropriate experimental set-
ups. Fracture occurs when a critical value of the intensity
factor is reached for a particular material.
3.2.3 Other Modifications and Developments
With Irwin's modification of Griffith theory to the
stress-intensity approach, research in fracture testing of metals
increased many-fold. In 1959, an ASTM special committee on
Fracture Testing of High Strength Metallic Materials was formed to
launch an intensive research effort on fracture, based on the
Griffith-Irwin theory (Weiss and Yukawa, 1964). Plasticity and
dynamic considerations were also evaluated.
Research and testing culminated in the development of ASTM
E399, which gives standardized test procedures for the
determination of fracture toughness. First set forth in 1964,
they were formally adopted in 1972.
3.2.4. Critical Appraisal of Approach
The Griff ith-Irwin approach to the study of fracture
initiation is now generally accepted but it is not without
drawbacks and deficiencies. An early argument against the


24
Griffith concept was the difficulty in determining reasonable
values for surface tension, which is vital to the concept. Irwin
managed to get around this objection by noting that work done
against plastic deformation is much more significant than surface
energy. For ductile materials, the theory appears to fail due
mainly to a large plastic zone relative to crack length. lastly,
some researchers have considered the possible existence of an
energy barrier to crack initiation.
Experience has shown that plasticity phenomena limits the
applicability of Griffith-Irwin theory. With smaller specimen
sizes, the plasticity zone becomes larger relative to crack
length, thus negating a basic premise of the theory that the
plastic zone be small relative to crack length.
Lastly, the theory was developed initially for glass,
which behaves in a nearly ideal manner relative to the Griffith
theory. Researchers were able to apply the theory to metals with
appropriate modifications and assumptions, and the Griff ith-Irwin
concept has proved effective with metals. Rock materials do not
possess the same basic material responses as metals and thus the
application of the theory cannot be straightforward. While
testing with metals may result in determination of material
properties, with rocks the situation is much less clear and
determination of material properties may not be possible.


25
3.3 T.inear Elastic Fracture Mechanics
3.3.1 Introduction
A linear elastic material is one for which the components
of strain are linear functions of the components of stress.
Strictly speaking, this condition must be true under all
conditions, but in reality, most materials will differ to seme
degree from true linear elastic behavior except for seme definable
range.
Fracture mechanics concerns the study of stress
concentrations caused by sharp-tipped flaws and the conditions for
the propagation of these flaws (Rudnicki, 1980). Linear elastic
fracture mechanics (IEFM) is the formulation of Griffith-Irwin
theory for materials with real or assumed linear elastic behavior.
Central to the field is the determination of the stress intensity
factor, K, which essentially describes the entire stress field at
a crack tip in a linear elastic material (Schmidt, 1980). Through
a study and evaluation of the stress intensity factor it is hoped
that a better understanding of failure can be obtained. Because
of an increasing recognition that materials can fail suddenly and
unexpectedly at stress levels well belcw their supposed failure
strength, the study of fracture mechanics became necessary.
3.3.2 Stress Intensity Factor
The geometry of a crack is such that a stress singularity
develops at the crack tip as stress is applied. The magnitude of
this singularity will depend upon the loading and geometry.


26
It is necessary to define a crack in a linear elastic body
before the stresses at the crack tip can be analyzed.
Essentially, a crack is a line of discontinuity in a displacement
field. The opposite sides of this line, the crack faces, may or
may not be stress-free. Cracks can deform in three basic modes,
as shown in Fig. 3 (Schmidt and Rossmanith, 1983). Mode I is the
opening mode, a common experimental mode, while Mode II is the
sliding mode, and Mode III is the tearing mode.
The stress intensity factor (K) is the intensity of the
stress singularity at a crack tip. When this factor reaches a
critical value (K,-,), the crack will advance. The critical value
has been determined to be a material property for numerous
materials, especially metals, and it has been shown to be the
controlling fracture parameter.
As previously discussed, Irwin modified the Griffith
theory and determined that the stress intensity factor is given by
K = (EGA) %. This was for a specific geometry, however, and it
can be shown that the crack tip singularity formulation will vary
according to loading configuration. The critical parameter, or
Kc, is called the fracture toughness.
The most commonly determined stress intensity factor is
that for Mode I plane strain conditions; it is termed the plane
strain fracture toughness, or KIc. For an elliptical flaw or
crack of length 2a in an infinite plate in tension perpendicular
to the plane of the crack, it can be shewn by Westergaard methods
of stress analysis that: Klc = ac(7ra) This can be related to


27
Fig. 3. Three basic inodes of deformation (Schmidt and
Rossmanith, 1983)


28
the Griffith concept where U is the strain energy due to the
presence of the crack, G equals the strain energy release rate
-(dU/da) and r is the surface energy of the crack. According to
Griffith, fracture advance at a crack tip occurs when G = 2r.
(The surface energy, r, may be replaced with reff if all
dissipative effects at the crack tip and its immediate
surroundings are included in r.) For a stress calculation for an
elliptical flaw in an infinite plate in tension,
dU/da = (7tct2 a) / E', with E' = E (Young's modiolus)
for plane stress and
E' = E / (1 v2)
for plane strain, which means that
G = (no2 a / E') =2r.
Crack or fracture advance occurs at a critical value, Gc,
therefore, Gc = (iroc2 a) / E'.
But Klc = ac(7ra)^, so:
Gc = (Kic)VE for plane stress conditions,
and
Gc = [(Klc)2/E][l v2] for plane strain conditions.
Units of fracture toughness are stress times the square
root of the crack length, often expressed in a somewhat confusing
form such as lb-in-3/2, more appropriately expressed as psi/m.
Failure criteria can be based on fracture toughness, thus
accounting for the loss of load-carrying capacity due to the
presence of flaws. However, difficulties arise in the detection
of flaws and thus failure prediction can be difficult.


29
3.3.3 Crack Tip Zone
3.3.3.1. Plastic Zone in Metals
It is necessary to understand the conditions at the crack
tip if all aspects of the fracture process are to be understood
(Weiss and Yukawa, 1964). From a linear elastic analysis of
stresses at a crack tip, it can be shown that the stresses became
infinite for all non-zero values of K (Schmidt and Rossmanith,
1983). This is an unacceptable condition indicating that the
model is not accurate for crack-tip conditions. Nonlinear
behavior, usually of a plastic nature in metals, is taking place
at the crack tip, allowing the stresses to be finite. As long as
the plastic zone remains relatively small, however, the IEFM
analysis is valid.
Conditions at the crack tip are actually a combination of
two separate sets of conditions. The first relates to conditions
in a very small localized region near the crack tip which are
necessary to initiate unstable fracturing, while the second
involves conditions more remote from the crack tip which are
necessary to sustain unstable crack motion once the initiation
condition has been fulfilled. The material offers resistance to
these conditions and the stress intensity factor is a measure of
this resistance. Strains in the plastic zone, then, will be
dependent only on the stress intensity factor (Weiss and Yukawa,
1964).


30
3.3.3.2. Micro-cracking Zone in Rocks
The non-linear crack-tip behavior in rocks is manifested
by micro-cracking and the development of a zone of micro-cracking
at the crack tip. Again, as with metals, as long as this zone is
relatively small, the crack tip stress field is still largely
defined by elastic behavior and crack growth will occur when K
reaches K,-..
The size and shape of the plastic zone in metals or the
zone of micro-cracking in rock cannot be determined precisely. An
approximation can be obtained, however, by applying a Von Mises
yield criterion, given as:
(cti o2V + (a2 a3)2 + (a3 c^)2 = 2(ays)2
(CTyS = uniaxial tensile yield stress)
For Mode I conditions, the principal stresses are:
01 = (V(27rr)^) (cos(9/2) (1 + sin(0/2)))
02 = (K/(27rr)^) (cos(0/2) (1 sin(/2))
a3 = v(a! + a2) (for plane strain)
Substituting into the yield criterion and solving for r gives the
shape of the plastic zone:
r(0) = (1/4tt) (K/ays)2 [(3/2)sin20 + (l-2v)2 (1 + cos0)],
(for plane strain)
and as shewn in Fig. 4 (Schmidt, 1980). This solution is not
entirely valid, because if the stresses within the plastic zone
are limited to the yield stress, the stresses outside the zone
must increase and thus increase the actual plastic zone size.


31
PLANE
r
2
Fig. 4. Shape of plastic zone with Von Mises yield
criterion (Schmidt, 1980)


32
For metals, the apparent fracture toughness will vary
according to crack length and this is a reflection of the relative
size of the plastic zone. ASTM has set a criterion for metals,
for a valid test of Kjc, that the crack length be equal to or
greater than 2.5 (KIc/ayS). A thickness effect is also
controlling the validity of a test. For rock, fracture toughness
also depends on crack length but doesn't appear to be affected by
thickness.
Micro-cracking in rock occurs as a result of tensile
stresses while plasticity in metals results from shear stresses
(Schmidt, 1980). An estimate of the zone of micro-cracking in
rock can be derived using a maximum normal stress criterion given
as o-y = uu when ctu is the ultimate tensile strength. Solving for
r gives:
r(0) = .57r(iyau)2 [cos(0/2) (1 + sin(0/2) ]2
as shown in Fig. 5 (Schmidt, 1980). The actual zone will be
larger than the theoretical zone, as was the case with the plastic
zone in metals.
Though analogous, the plastic zone in metals and the
micro-crack zone in rocks have two distinct differences. The
micro-crack zone remains unchanged no matter what the value of the
out-of-plane stress (a3) is. Possibly this is why there is no
apparent thickness effect with rocks. Also, under hydrostatic
compression, the plastic zone in metals will remain unchanged but
the micro-crack zone in rocks will decrease in size, indicating a
probable increase in Kjc for rocks under hydrostatic compression.


33
_r
JL
'U
7
Fig. 5. Shape of microcracking zone with maximum normal
stress yield criterion (Schmidt, 1980)


34
For an effective determination of fracture toughness, Kjc,
with metals or rock, plasticity corrections should be made. For a
thorough evaluation of these, the reader is referred to Barker
(1977b) and ASTM E399 (83). Generally, however, it is sufficient
to assume strictly linear elastic behavior and ignore plasticity
effects.
3.4 Short Rod Specimen Testing
3.4.1 Introduction and Background
Numerous test procedures have been devised for the
determination of fracture toughness of metals and other materials.
Metals testing procedures are summarized in ASTM E399, which was
first adopted in 1972. The ASTM test procedure sets out a
stringent list of criteria which must be met in order for testing
to be valid according to LEFM principles. Testing of materials
according to this ASTM standard tends to be a relatively expensive
and involved procedure. For this reason, other, more simple
methods were developed.
Barker (1977a) introduced a new method of measuring a
material's critical stress intensity factor, Klc, or plane strain
fracture toughness, based on a rod-shaped test specimen. The
specimen is pre-notched and allows crack growth stability during
the first phase of crack growth.


35
3.4.2 Theoretical Basis
Barker (1977a,b) set forth the theoretical basis for the
short rod specimen configuration and the following is a summary of
his argument.
The general sample configuration is as shown in Fig. 6
(Barker, 1977b). The specimen is pre-notched or slotted such that
as load is applied as shown in Fig. 7, the crack will initiate at
the point of the "V or chevron tip. As the crack propagates, the
sample will split in the plane defined by the notch.
Assuming plane-strain conditions at the crack tip, the
crack will not advance if: b Gjc > (^),
2 da
where Gjc is the plane-strain critical strain energy release rate,
b is the crack width, F is the applied force, and c is the
specimen compliance defined by c = y/F at the crack position a. Y
is the slot opening distance at the face of the sample due to the
force F.
Increasing F leads to a point at which the crack will
advance. The crack will arrest only if:
*j- (Kiel >£- da da 2 da
If Gjc is assumed to be a material constant and F is held constant
as the crack advances:
Gic (?) > (FV2) (ff)
da da2
This is the condition for crack growth stability (crack arrest).
From Fig. 8, db/da = b/(a a,-,) and at the time the crack
begins to grow, F2 = 2bGIC/ (dc/da). Therefore the crack growth


36
Fig. 6. Short rod specimen configuration (Barker, 1977b)


37
Fig. 7. Load application for short rod specimen (Barker,
1977b)


38
SLOTTED
SURFACE
W--------H
Fig. 8. Nomenclature for theoretical analysis of short
rod specimen (Barker, 1977a)


39
stability condition becomes:
dc/da > d2 c
a a0 da2
At a = ac, the crack growth becomes unstable under
controlled-force loading and the crack suddenly propagates the
remainder of the length of the specimen. Thus, at a = a^-, the
above becomes:
(d(cE)/da)/(a a0) = d2 (cE)/da2 (multiply by E)
Barker (1977a) showed that ac is the solution to this
equation and can be considered independent of the specimen
material properties and dependent only on the specimen geometry.
As the load on the test sample is increased and a reaches
a^., the load reaches a critical value Fc. Just as the sample
breaks,
A2 = GjcEB3 / Fc2,
where A2 = (B3/2bc) [d(cE)/da]a=ac
(B is the specimen diameter; b = bc when a = ac) and A can be
calculated. A is a dimensionless parameter introduced to
facilitate calculation of the fracture toughness. As long as the
geometrical proportions are the same, A will always remain the
same regardless of the actual specimen size.
For isotropic materials, GjcE = (Kjc)2 (1 v2). If a
standard material of known Klc is tested using the standard
geometry, A can be determined and used to calculate Klc for other
materials through:
Klc = AFC / [B3/2(1 v2)^]


40
In the above derivation, based on traditional assumptions
of linear elastic fracture mechanics (IEFM), the dimensions of the
specimen are assumed to be large enough, compared to the size of a
plastic or microcracking zone at the crack tip, that the gross
specimen behavior is as if the zone did not exist. Generally, is
true, but with smaller specimens, it may not be the case. Barker,
therefore, introduced a modification of the above analysis for
elastic-plastic specimen behavior. The reader is referred to his
paper (Barker, 1977b) for the complete analysis.
3.4.3 Critical Appraisal
Barker (1977a) found good agreement between published
values of Kjc and those he obtained with short-rod specimens,
indicating basic validity in the test method. However, he did
recognize the need for further testing as well as the evaluation
of questions arising from the differences of his specimen geometry
from established test geometries.
ASTM standard methods (E399) are based on the onset of
crack position instability, whereas the short rod test is based
upon crack growth instability. In the short rod test, the stress
intensity at the crack tip is always equal to KIc. Barker (1979)
presents the argument that the ASTM methods are (and must be)
actually based on a steady-state crack-tip configuration, which is
also the case for the short rod test configuration.
ASTM test procedures for fracture toughness have a minimum
size requirement. This tends to lead to the use of rather large


41
test specimens, especially with metals. However, with many other
materials it may not be possible to lose large test specimens. The
size criterion was deemed necessary in order to assure plane-
strain conditions and nearly perfect elastic response. As
specimen size decreases the response may change from elastic to
elastic-plastic, thus invalidating, at least in theory, the Klc
measurement.
It has been found (Barker, 1979) that very thin slots
along the sides of the specimen can serve to maintain plane strain
conditions along a crack tip, even in test specimens which are
undersize according to ASTM requirements. It is still necessary,
however, for the size of the plastic zone at the crack tip to be
small compared to the dimensions of the test specimen. Barker
(1984) determined a minimum size requirement of B > 1.25 (Klc/at)2
for the short rod specimen, where B is the specimen diameter and
ct-j- is the unconfined tensile strength of the material.
Testing a specimen with displacement-controlled
conditions, it is possible to load the specimen to a steady-state
crack-tip configuration, pass it through two or three unload and
reload cycles, and determine a plasticity correction from the
load-displacement curve (assuming that the specimen is behaving in
an elastic-plastic behavior and not strictly elastic) (Barker,
1977b, 1979). Therefore, Klc could be measured on a specimen
exhibiting seme elastic-plastic behavior during a test, generally
due to sub-ASTM-standard dimensions. Barker (1979) showed that
even with a 12.7 mm diameter specimen, good agreement in test


42
values of KIc with tests of larger specimens was obtained,
indicating a size-independence of the parameter. It appears that
for short-rod specimens, the ASIM size criteria are not valid.
For chevron-notched specimens such as the short rod, the
stress intensity factor is very large at the vertex of the notch
and thus only a small load is necessary to initiate a crack
(Karfakis, et al., 1986). The stress intensity factor passes
through a minimum as the crack grows, providing the initial
stability of crack growth. K will equal Klc when the crack-
driving curve is tangent to the resistance curve. (See Fig. 9).
Disadvantages of the test configuration include
difficulties in machining the notches and a restriction to lew
toughness (brittle) materials (Karfakis, et al., 1986).
3.5 Application of Toughness Testing to Rock
Increased interest in the study of rock fracture has led
to efforts to apply metals testing techniques to rock. Rock
generally does not exhibit fracture behavior similar to metals but
analogies can be made. Also rock tends to be anisotropic in its
behavior, resulting in different fracture behavior depending upon
the test orientation relative to any anisotropy. ASIM test
standards for metals cannot be strictly applied to rock testing.
Probably the most significant difference between rock and
metals is that in metals a crack tip is characterized by a zone of
plastic deformation, while in rocks the zone is an area of intense
micro-cracking. Although somewhat analogous and similar in


43
Crack length, a
Fig. 9. Stress intensity minimum versus crack opening
resistance (Newman, 1984)


44
overall behavior, the zones are not, in theory, the same. Rock
also tends to be more easily influenced by environmental factors
such as temperature and moisture. Moisture facilitates stress
corrosion cracking leading to an overall lowering of rock
strength. Recognition and control of these factors, however,
allows fracture testing to be done on rock.
Rock is not a true linear-elastic material, so, strictly
speaking, IEFM principles cannot be applied. However, as with
metals, if fracture test procedures are done such that the micro-
cracking zone at the crack tip is very small compared to the other
specimen dimensions, a siirplifying assumption of linear-elastic
behavior is valid. Barker's (1977b, 1979) plasticity correction
for short rod specimens is especially useful because it allows for
some inevitable deviation from linear-elastic behavior.
Metals testing procedures involve elaborate machining of
specimens, a condition that is not readily adaptable to rock,
although early researchers with rock tended to try to very
carefully duplicate metals testing configurations. Rock generally
is available as core and thus test specimen configurations based
on core geometry are desirable. Over the past few years there has
been a strong trend towards using chevron-notched, three-point
bend, and short-rod configurations for rock testing. Ingraffea
(1985) gives an excellent summary of test configuration evolution
and their use. With the adoption of rational test procedures for
rock fracture toughness measurement, techniques for employing the
information in analytical models can progress.


CHAPTER IV
TEST PROCEDURES
4.1 Purpose of Testing
The primary aim of testing was to determine fracture
toughness values under various physical and environmental
conditions. Test variables included density, temperature of
heating, and the presence or absence of water. Data would be
evaluated in order to make conclusions as to the relative
influence of each variable.
Inherent in the test program was to be an overall
evaluation of the proposed ISRM procedures for fracture toughness
determination of rock using core-based samples. This evaluation
would be from the viewpoint of a practicing engineer with typical
geotechnical laboratory facilities at his disposal, as opposed to
the viewpoint of a researcher with more sophisticated equipment
available.
The discussion of test procedures is broken down into four
parts, these being, (1) a discussion of test specimen preparation,
(2) a discussion of the actual test procedures, (3) a discussion
of data handling and reduction, and (4) a critique of the methods
used and the problems encountered.


46
4.2 Test Specimens
4.2.1 Test Material
It was desired to base the testing on a volcanic tuff
either from the proposed Yucca Mountain high-level nuclear waste
repository site at the Nuclear Test Site (NTS) in Nevada, or as
similar a tuff as could be obtained from other sources. It was
not possible to obtain tuff from the NTS, but a somewhat similar
material was obtained from a locality near Gunnison, Colorado
through Jacobs Engineering in Albuquerque, New Mexico.
The test material consists of a crystal-rich rhyolitic
tuff. It was available in the form of NX wireline core (nominal
1.875" diameter). Sufficient core was available to prepare three
groups of 40, 39, and 40 specimens each, respectively.
4.2.2 Specimen Preparation
Specimen preparation began with an examination of the
available core to determine the general degree of variability in
the material. It was initially determined that at least three
density groups could be made up from the material. Densities
ranged from near 100 pcf to over 140 pcf, but tended to cluster
around certain densities. After same trial and error, the density
ranges chosen for testing were:
Group A: 110 115 pcf
Group B: 120 125 pcf
Group C: 130 135 pcf


47
Once the density groups were established, it was necessary
to find sufficient material in each range to allow for five
specimens for each test criteria.
Chosen core material was first cut to a length of between
2.75 and 3.0 inches on a diamond-blade saw. Some material was cut
wet and some was cut dry, depending upon the particular saw
available. Specimens were then mounted in a vise and the ends
were ground using a grinding wheel mounted on a milling machine.
The grinding set up is illustrated by Fig. 10. Both faces were
ground parallel to each other and perpendicular to the core axis.
Final length was in the range 1.45 D .012 D, where D is the
specimen diameter.
After grinding, the specimens were weighed and measured
and then given a chevron notch using a thin diamond rock saw blade
and a special holder which allowed the specimen to be rotated 180
on its axis so that, with two passes over the blade, the chevron
notch was formed in the specimen. Initially, the slots were
formed by dry cutting but a special device was made which allowed
water to spray on the blade periodically to provide lubrication
and cooling for the blade without excessive soaking of the
specimen. The cutting device and related attachments are shewn in
Figs. 11 and 12. Notch widths varied from .040" to .060",
depending on cutting methods and the particular blade thickness
used.
Final specimen preparation consisted of epoxying two
aluminum plates to the notched end of the specimen. These plates


48
Fig. 10. Set-up for grinding ends of short rod specimens


49
Fig. li. Set-155 for cutting notch in short rod specimens


50


51
provide a means of applying an opening force to the notch in a
direction normal to the notch plane and in the plane of the end of
the specimen. Figure 13 illustrates the sequence of attaching the
plates.
4.2.3 Petrographic Examination
Samples from each density group were examined
petrographically to determine their lithology and texture. Thin
sections were prepared from one representative specimen from each
core hole represented in each density group. These were then
examined under a polarizing light microscope, using both plain and
polarized light.
Utilizing the microscope, major and minor constituents
were identified, estimates of component percentages were made and
textural features were identified and evaluated. Particular
attention was paid to anisotropies and degree of welding. Using
the microscopic data, the rocks were identified and given a
complete lithologic description.
4.3 Test Procedures
4.3.1 ISRM Level I Testing
Test procedures were based on the ISRM "Suggested Methods
for Determining Fracture Toughness of Rock Material," 4th draft,
dated June 1, 1986. The methods utilize core-based specimens with
two configurations, the chevron-notched bar-in-bending, and the
chevron-notched short rod. For each configuration, two levels of
testing are available. Level I testing requires only the


52
j ;V >
ty. j. v < k-<
ija
^iUlTO'
THwiminrrrua
ihi!i!SHiTitiiri-"ij-L^

* ' -4 -

Fig. 13. Procedure for attaching end plates to
short rod specimens


53
measurement of a peak load for fracture toughness calculation,
while Level II testing requires the recording of a complete load
displacement curve with at least two unload cycles. Level I
Testing requires only load control but level II testing requires
displacement (strain) control. For the purposes of this study,
the short rod configuration and Level I testing were chosen
because of the relative ease of preparation and testing, and
because precise values of K were not required.
Briefly, level I testing of chevron-notched short rod
specimens consists of attaching grips to the end plates of the
specimen. Using load control, the grips are pulled apart. A load
cell in line with the grips registers the splitting load. The
test set-up used for this study is shown in Fig. 14. The peak
load attained is recorded for calculation of the fracture
toughness. Generally, the sample is allowed to split fully in
order to observe the fracture surface. The ISRM procedure for
fracture toughness testing of rock is presented the Appendix.
4.3.2 Heat Effects
One purpose of the study was an evaluation of the effects
of uniform heating of the rock on measured fracture toughness.
Ideally, the rock should be tested while at a certain temperature.
This was impractical considering the equipment available, so
testing was done on specimens heated to a specific temperature in
an oven and then allowed to cool back to room temperature ( 25C)
before testing. Testing, then, actually measures the residual


Fig. 14. Apparatus for Level I short rod fracture
toughness tests


55
effects of heating and not necessarily the full effects of
heating.
Sample preparation consisted of placing the test group of
specimens in an oven at the chosen temperature level, either 50,
100, or 200C, and holding them at that temperature for 24 hours.
The specimens were then removed from the oven and allowed to
slowly cool to room temperature. Specimens were then tested in
the same manner as described in the previous section, with peak
splitting (fracture) load being recorded.
4.3.3 Water Effects
The effect of water on the fracture toughness of the tuff
was studied by immersing the test specimens in water for 24 hours
prior to testing. This was intended to give water full access to
the crack tip during testing, but was not intended to fully
saturate the specimens. Actual degree of saturation would depend
upon effective porosity and degree of microcracking in the
specimen. Free access of water to the crack tip could approximate
the presence of water at the cutter head of a tunnel boring
machine or at the tip of a rock drilling bit. As with other
testing, the peak load was recorded for Kjc calculation.
4.4 Data Handling
4.4.1 Data File
Due to the large amount of data generated by the sample
preparation and testing process all data was placed into, and
processed by, a Lotus 1-2-3 (v.2.0) worksheet file. Using the


56
file, it was also possible to perform statistical analyses of
certain parameters and create x y plots as necessary.
Data entered into the file included the specimen length,
diameter, weight and density group. As data was entered, the
density was calculated and dimensional tolerances according to the
draft ISHM test procedures were determined. A "YES" or "NO"
indication was then automatically placed in the file if the sample
did or did not meet one or more of the dimensional tolerances.
After testing, the notch width, temperature of the test, test
condition (wet or dry), and the peak load were entered into the
data file. The notch width was compared to the tolerance given in
the ISRM test procedures and a YES/NO compliance determination was
given. The fracture toughness, Klc, was calculated automatically.
After completion of all the testing, each data set was
evaluated to determine a mean and standard deviation for the set.
Means for a given density group were then plotted to allow
comparison. Other graphical plots and comparisons were made as
necessary.
4.4.2 Data Calculations
A number of calculations were required to effectively use
and evaluate the data.
Density was calculated in pounds per cubic foot (pcf) from
the length, diameter, and weight of the specimen. All samples
were air dried for a minimum of 24 hours prior to weight
determination.


57
ISEM test procedures for fracture toughness of rock give
tolerances for the specimen length and the chevron tip position
based upon the specimen diameter, D. The specimen length must be
1.45D .02D; the tip position must be .048D .02D. The optimum
and actual values were calculated and compared. Based on the
comparison an entry of "YES" or "NO" was placed in the data file
to indicate whether or not the specimen met the required
tolerances.
For Level I testing, fracture toughness is calculated
according to:
%R = (24* W/D15'
where Kgp indicates short rod fracture toughness.
This equation is essentially identical to the equation
derived by Barker (1977a,b) to evaluate short rod fracture
toughness (see section 3.4.2). In Barker's analysis, B designated
the specimen diameter; here D designates the diameter. The term
(1 v2)^ has been replaced by 1. The term, A, in Barker's
equation, is replaced by 24.0, which has been found by experiment
and computer analysis to be the best consensus value for A
(Ouchterlony, 1985; Newman, 1984) for the short rod specimen with
standard, dimensions given in the draft ISKM test procedures.
A correction factor is then determined from:
CK = 1 0.6(aw/D) + 1.4(AaQ/D) 0.01(A)
where Aw, Aa0 and A denote the differences between the measured
values of length (w), initial chevron tip position (a0), and
chevron angle (20), and the nominal values. For example,


58
W/D = (w 1.45D) / D
(Note that the nominal values for the draft ISKM test procedures
will be presented in a later section.) A comprehensive derivation
of this correction factor is presented by Oudhterlony (1985). If
0.99 < CK < 1.01, the fracture toughness value as originally
calculated is valid, otherwise it is recalculated from:
Ksr = Ck(24.0 WJ/D1-5
For this study, w and a0 were measured but 6 was
calculated from the relation:
tan 6 = ^D(a;L a0),
where a-^ is the maximum depth of the chevron flanks (generally a^
equals w, the specimen length). Correction factors and resultant
corrected fracture toughness values are given in the data tables.
The mean and standard deviation for densities and fracture
toughness values were calculated by standard formulations. Other
statistical calculations were made as necessary in order to
evaluate the data. Calculated values were automatically entered
into the data file for future lose.
4.5 Critique of Procedures
4.5.1 Test Specimen Preparation Difficulties
Numerous difficulties of varying severity were experienced
with test specimen preparation. These included problems with
specimen trimming, grinding, and notch cutting.
Specimens were cut to rough length on a diamond-bladed saw
after selecting suitable material from the available core. Three


59
different saws were used. A 10-inch tile saw was first tried.
Samples were cut wet and had to be fed to the saw blade by hand, a
rather messy and potentially unsafe procedure. Some cutting was
done on a 16-inch brick saw with and without water, again with
manual feed. Both methods allowed for rapid cutting but produced
cuts that were generally many degrees off of being perpendicular
to the core axis. A third saw used was a diamond-bladed rock saw
with automatic feed. Specimens were held by a vise and fed slowly
into the blade. Specimens could be cut either wet or dry. This
method was much slower than the other two but generally produced
cuts much closer to being perpendicular to the core axis,
especially if the cutting was done with water and the feed table
was carefully aligned with the blade. Dry cutting of cores tended
to result in blade wander or deflection, especially in the denser
samples. None of the three saws used produced cuts that were
close enough to being perpendicular to the core axis that
subsequent grinding was not required.
The three saws used are probably typical to what would be
available in an average soils-oriented laboratory. Laboratories
specializing in rock testing might have more precise equipment,
but such labs seem to be few in number. An ideal set-15) for
cutting samples to length is a lathe with two parallel blades set
to the required sample length. Core is fed to the blades by a
holder on a cross-feed table. The resulting cut specimen is ready
for testing without additional grinding of the ends. This sort of
set-up was first described by Bieniawski (1967).


60
For this study, all specimens had to be end ground to
produce a specimen of the proper length with ends parallel to each
other and perpendicular to the specimen axis. A milling machine
with a grinding wheel attached to a suitable mount and mounted in
a chuck, as previously shown in Fig. 10, was used for the grinding
process. A vise held the specimens such that their axis was
parallel to the axis of rotation of the grinding wheel. Passing
the grinding wheel over the end of the specimen produced a surface
perpendicular to the core axis.
Grinding was a slew and time-consuming process, taking as
much as a half hour to grind the two ends of a specimen. Wear and
heat build-up on the grinding wheel, as well as inprecision in the
mill made it nearly inpossible to grind the specimen ends truly
perpendicular to the core axis. Minor irregularities in the core
compounded the problem. The ISRM test procedures do not call for
the specimens to meet stringent parallelity and perpendicularity
criteria, but conditions must be reasonably close to idea.
Again, the mill used for grinding may be typical or better
than what would be available in an average soils lab. A better
arrangement is a surface grinder, but these are often not
available. With a proper saw arrangement, however, grinding would
not be required in most cases.
Cutting the chevron notch in specimens proved to be a
sensitive and tedious process. A holder w/as prepared according to
suggestions in the ISRM draft test procedures. This w/as then
mounted on the moving carriage of a rock saw. The set-up w/as


61
shown previously in Figs. 11 and 12. With proper adjustments, the
specimen could be fed over the diamond saw blade producing half of
the chevron, then turned 180 degrees and passed over the blade
again to complete the chevron notch. This process proved to be
highly sensitive to several factors. First, the saw mechanism had
to be carefully aligned and free of excess slack or slop in the
various mechanisms. Undetected slop in the feed table resulted in
numerous specimens being rejected due to mis-aligned cuts.
Cutting was first attempted dry, but the blade tended to deflect
out of alignment. This, combined with blade wobble, produced
notch thicknesses too great to meet suggested tolerances. After
much trial and error, a blade diameter of 8 inches and 0.032"
thickness was settled upon as being able to produce a final cut of
0.050" using a water spray for cooling. A special device was
developed which would periodically spray the blade with water to
cool it, but keep the wetting of the specimen to a minimum. Blade
wander was still a nagging problem, due in part to the
impossibility of getting the moving table and blade in truly
perpendicular alignment, so not all specimens were grooved
successfully. It is estimated that at least 20 to 25 percent of
the specimens prepared were ruined during the notching process.
This can be an unacceptable condition if available core is limited
and, indeed, it eventually proved difficult to obtain enough
specimens for one of the density groups.
The ISRM test procedure for rock fracture toughness is
meant to make the testing more universally available and


62
potentially make it available for on-site testing for engineering
projects in rock. If, however, it is difficult to prepare
adequate specimens with average equipment, such a goal may not be
possible. Studies need to be made of the effect of mis-alignment
of the two cuts necessary to produce the chevron notch to
determine just hew sensitive the test results are to this
condition, particularly with Level I testing.
4.5.2 Test Procedure Difficulties
Test equipment for Level I testing is relatively simple.
Grips as illustrated in Fig. 15 and 16 can be vised, or more
elaborate grips as shewn in the ISFM draft procedures can be used.
Neither are available commercially and so must be specially made.
The grips, along with a load cell of an appropriate range can be
mounted on a modified unconfirmed compression frame, as shewn
previously in Fig. 14. Testing is accomplished by moving the
grips apart using the hard crank and recording the peak load.
Alternatively, a device such as developed by Ingraffea, et al.
(1984) can be utilized.
Testing is straight forward, although care must be given
to noting the peak load. With an electronic load cell, the signal
can be fed to a chart recorder and the peak load can be readily
determined. With weaker rocks, there is a strong tendency for the
advancing crack front to migrate out-of-plane and invalidate the
test. Ingraffea et al. (1984) has used clamps to strengthen the
ligaments and thus lessen the tendency to migrate out of plane,


63
Fig. 15. Fracture toughness test grips


64
.^ WJ- -LidTOire toughness
with specimen In place


65
but such clamps cannot be used with the ISRM-type grips. Further
studies are needed of the determination of fracture toughness of
weak rocks and hew it can be accomplished and if even it is valid.


CHAPTER V
TEST RESULTS
5.1 Introduction
A total of 119 samples of rock core have been tested for
their short rod fracture toughness under various test conditions.
An additional 42 samples of core have been tested for Brazilian
tensile strength. Thirteen core samples have been examined
microscopically by the use of thin sections to determine the
petrographic characteristics of the rock. Additionally,
previously determined data on uniaxial compressive strengths,
Young's modulus, Poisson's ratio and Brazilian tensile strength
were made available to the study.
5.2 Physical Properties
5.2.1 Petrographic Description
5.2.1.1 Source
The rock used for this study is a volcanic tuff from a
site about 2 1/2 miles south of Gunnison, Colorado. The site is
shown in Fig. 17. The core was obtained from Jacobs Engineering
Group in Albuquerque, New Mexico. The core had been drilled as
part of a uranium mill tailings reclamation study for the NRC, but
was no longer needed for that study.


1000 2000 3000 4000 5000 6000 7000 FEET
Fig. 17. Source location of tuff used for study


68
A published geologic map is available for the area
immediately south of the core hole locations. According to the
mapping (Hedlund and Olson, 1974), the tuff of this study appears
to correspond to the Oligocene Fish Canyon Tuff. The tuff
unconformably overlies preCambrian quartz-biotite schists and
gneisses and possibly remnants of Upper Jurassic Morrison
Formation sandstone and mudstone. The tuff may also overlie
Oligocene gravel deposits. As mapped by Hedlund and Olson (1974),
the Fish Canyon Tuff may be as much as 350 feet thick and consists
of a devitrified crystal rich welded tuff. Welding ranges from
light to dense. Generally, the tuff contains 25 to 40 percent
crystal fragments, mostly of calcic plagioclase and sanidine.
Biotite is a common and conspicuous consituent.
5.2.1.2 Macroscopic Features
In hand specimen the tuff is white to light gray in color.
Crystals of black biotite, gray feldspars, and gray quartz are
visible. Crystals generally range up to 3 to 4 millimeters in
size but more commonly are in the 1 to 2 millimeter size range.
Soft chalky pumice is scattered throughout the rock, ranging in
size from under 1 mm to over 10 mm. Volcanic ash and glass appear
to comprise the bulk of the rock, although crystals and pumice
generally comprise 40 to 50 percent of the rock volume.
Occasional lithic fragments are seen in the tuff. These range
from crystalline to sedimentary rock types and often are 10 to 20
mm in size. In seme specimens, a weak to strong foliation is


69
evidenced by planar orientation of the biotite crystals. This
foliation tends to be perpendicular to the core axis.
5.2.1.3 Microscopic Features
Thirteen specimens of tuff were examined microscopically
by the use of petrographic thin sections under plane and polarized
light. One thin section was prepared from each of the core holes
represented in each of the three test groups. Three additional
thin sections were prepared from one cracked fracture toughness
test specimen from each test group. Thin sections were examined
using a Nikon petrographic microscope provided by the Geology
Department of the University of Colorado at Denver.
Rock specimens were examined microscopically to determine
their major and minor constituents, microscopic features and
degree of welding. Cracked specimens were examined to evaluate
the crack path geometry and physical conditions.
Results of the microscopic examination are summarized in
Table I. Generally, the tuff is a rhyolite crystal tuff. Crystal
fragments comprise 40 to 50 percent of the volume of the rock.
Sanidine (potassium feldspar) and plagioclase (sodium-calcium
feldspar) are the dominant crystals present and are generally
present in roughly equal amounts. Quartz is present to a lesser
degree. Biotite, altered hornblende, opaque minerals and
accessory minerals comprise the remainder of the crystal portion
of the rock. Crystals are present as irregular fragments and
subhedral crystals.


O O O ca ffl 03 > > >
TABLE I
GROUP
SUMMARY OF THIN-SECTION PETROGRAPHIC EXAMINATION
| GRAIN ' CONSTITUENTS 1
HOLE DEPTH CRYSTAL QTZ SAN PLAG BIO HBLD OP PUM WELDING
ft % % % % % % % %
551 89.6 40-50 5 10-15 20-25 3-5 1-2 1-2 <1 SL
553 82.9 40-45 5-10 10-15 20-25 2 <1 1-2 <1 SL
554 97.1 40 10 10 15-20 2 2 1 <1 SL
551 101.0 40 5 15-20 15-20 2 1 1 <1 SL
552 53.4 40-50 5-10 15-20 15-20 2-3 1-2 1 1 SL
553 96.6 45-50 10 15-20 20-25 2 2 1 1 SL
557 15.1 40-50 5-10 15-20 20-25 2-3 2 1-2 1 SL
552 90.5 50-60 10-15 15-20 20-25 2-3 1-2 1 1-2 MOD
555 33.4 50 10-15 15-20 15-20 2 1 1 1-2 MOD
556 25.3 50 10-15 15-20 15-20 2 <1 1-2 1-2 MOD
QTZ=quartz
SAN=sanidine(potassium feldspar)
PLAG=plagioclase(sodium-calcium feldspar)
BIO=biotite
HBLD=hornblende
OP=opaque minerals
PUM=pumice
Remainder of rock mass is amorphous glass and pumice
Rock is a crystal-rich rhyolite tuff from a location south of Gunnison,
Colorado. It is probably from the Oligocene age Fish Canyon Tuff, as mapped
by Hedlund and Olson(1974).


71
The remainder of the tuff is comprised of pumice,
devitrified glass shards and volcanic ash. Welding of the glass
and ash varies from slight to moderate and is evidenced by
development of a foliation within the matrix of the rock and
draping of the foliation texture around crystal fragments.
Additionally, pumice fragments are flatter with increasing degree
of welding. In general, rock density increases with increasing
degree of welding.
Biotite flakes tend to form a planar alignment or
foliation, generally nearly perpendicular to the axis of the core.
Elongate crystal fragments tend to align themselves within the
plane of the foliation. The foliation also corresponds to welding
or compaction foliation observed in the denser tuff specimens.
Micropscopic observations of the crack path on crack
specimens indicate that the crack front tends to follow a path of
least resistance. One specimen from each density group was
examined. In Groups A and B, the crack remained entirely within
the matrix of the rock and was observed to never cut across a
crystal grain. The crack tended to follow a saw-tooth-1 ike path
as it progressed around crystal grains. In Group C, however, the
crack was observed to cut across several crystal grains.
5.2.2 Standard Properties
5.2.2.1 Density
Densities of all fracture toughness and Brazilian test
specimens were calculated from the physical measurements (length,
diameter and weight) of each specimen. Densities of fracture


72
toughness and Brazilian test specimens are summarized in the data
tables. Specimens were chosen such that the densities would fall
within one of the three chosen density ranges. All densities were
determined on air dried specimens.
Densities of fracture toughness specimens in Group A
ranged from 111.3 pcf to 115.1 pcf, with a mean of 113.4 pcf.
Densities for Group B specimens ranged from 119.7 pcf to 125.3 pcf
with a mean of 122.4 pcf. Group C ranged from 130.1 pcf to 135.0
pcf with a mean of 132.6 pcf.
5.2.2.2 Water Content
In general, water contents of specimens was not measured.
Instead two specimens were prepared from each drill hole in each
test group to measure the water content of air dry specimens and
specimens immersed in water for 24 hours. Results of these
moisture tests are tabulated in Table II. Also included in the
table is an estimation of the degree of saturation of each
specimen, based on an assumed average specific gravity as noted.
5.2.3 Strength Properties
5.2.3.1 Uniaxial Compressive Strength
The uniaxial compressive strength, compressive Young's
modulus and Poisson's ratio were determined for five specimens of
tuff. Results are tabulated in Table III. This work was done by
the author previous to the present study.
Young's modulus and Poisson's ratio were determined by the
use of a collar device shewn in Fig. 18, which measured axial and


TABLE II
MOISTURE DETERMINATIONS
AIR DRY AIR DRY
GROUP HOLE DEPTH LENGTH DIAMETER WEIGHT DENSITY
ft in in gm pcf
25 A 551 88.30 2.364 1.873 192.97 112.86
DEG A 553 79.90 2.652 1.868 217.22 113.86
C A 554 97.90 2.300 1.868 187.60 113.38
B 551 99.85 2.184 1.870 190.94 121.27
B 552 54.00 2.382 1.874 214.42 124.33
B 553 95.40 1.762 1.865 154.81 122.53
B 557 14.60 1.837 1.874 161.39 121.34
C 552 89.55 2.298 1.878 220.36 131.88
C 555 34.40 2.230 1.870 216.85 134.88
C 556 27.25 2.305 1.870 218.59 131.54
A 551 88.85 2.413 1.865 196.43 113.52
A 553 83.40 2.167 1.870 178.51 114.26
A 554 96.65 2.397 1.870 194.14 112.35
B 551 100.90 2.045 1.870 179.71 121.90
B 553 94.35 1.809 1.865 158.84 122.45
B 557 14.90 2.640 1.874 231.56 121.15
C 552 95.25 2.329 1.878 222.73 131.53
C 555 28.40 2.234 1.870 214.82 133.38
C 556 26.80 2.447 1.870 232.78 131.95
100 C 552 88.95 1.245 1.874 119.19 132.23
DEG C 552 93.15 1.153 1.877 110.43 131.86
C C 555 27.30 1.128 1.870 107.30 131.95
C 556 25.80 1.072 1.873 101.78 131.28
C 552 89.05 1.214 1.877 116.45 132.06
C 552 94.25 1.120 1.877 107.50 132.15
C 555 27.20 1.181 1.870 111.40 130.84
C 556 26.80 1.308 1.874 124.69 131.67
ESTIMATED MINIMUM SPECIFIC GRAVITY: GROUP A: 2.425
GROUP B: 2.485
GROUP C: 2.520
24 HR WET OVEN DRY AIR DRY WATER 24HR WATER INITIAL 24HR
WEIGHT WEIGHT CONTENT CONTENT SAT'N SATN
gm gm % % % %
N/A 189.91 1.6 N/A 10.8 N/A
N/A 214.26 1.4 N/A 9.6 N/A
N/A 184.63 1.6 N/A 10.9 N/A
N/A 188.64 1.2 N/A 10.3 N/A
N/A 211.25 1.5 N/A 14.0 N/A
N/A 153.04 1.2 N/A 10.2 N/A
N/A 158.80 1.6 N/A 13.5 N/A
N/A 217.47 1.3 N/A 16.0 N/A
N/A 213.73 1.5 N/A 20.1 N/A
N/A 216.34 1.0 N/A 12.6 N/A
221.14 193.11 1.7 14.5 11.7 98.7
200.33 175.61 1.7 14.1 11.5 98.4
219.82 190.59 1.9 15.3 12.1 99.8
197.26 176.91 1.6 11.5 13.4 97.6
174.54 156.59 1.4 11.5 12.5 99.9
255.46 227.84 1.6 12.1 13.5 99.9
237.01 218.97 1.7 8.2 20.0 95.8
227.98 211.33 1.7 7.9 20.9 99.8
247.99 229.38 1.5 8.1 17.8 97.4
N/A 117.19 1.7 N/A 20.5 N/A
N/A 108.58 1.7 N/A 20.1 N/A
N/A 105.67 1.5 N/A 18.5 N/A
N/A 100.11 1.7 N/A 19.2 N/A
123.90 114.48 1.7 8.2 20.5 97.9
114.44 105.66 1.7 8.3 20.8 99.1
118.86 109.66 1.6 8.4 18.1 95.5
132.89 122.53 1.8 8.5 20.6 98.7
U>


74
TABLE III
TUFF STRENGTH DATA
BRAZILIAN UNIAXIAL
HOLE NUMBER DEPTH (FT) DENSITY (PCF) YOUNG'S MODULUS (PSI) POISSON'S RATIO TENSILE STRENGTH (PSI) COMPRESSIVE STRENGTH (PSI)
552 24.0 107.3 5.8E+05 0.08 332 2440
556 8.5 132.6 2.2E+06 0.16 1050 10900
556 49.0 133.8 2.5E+06 0.1 1220 8720
557 10.8 117.9 8.1E+05 0.1 573 4070
558 19.0 95.5 1.2E+05 0.04 260 1460
(DATA FROM TESTING DONE FOR JACOBS ENGINEERING GROUP, ALBUQUERQUE, NM,
BY CHEN & ASSOCIATES, INC., DENVER, CO.; USED UITH PERMISSION)


75
Fig. 18. Rock deformation collars for determination of
Young's modulus and Poisson's ratio


76
lateral strains by averaging the readings of six LVDT's evenly
spaced around the circumference of the sample. Three LVDT's
measured axial strain and three measured lateral strain. The
LVDT's could measure to 0.0001 inch.
5.2.3.2 Brazilian Tensile Strength
The Brazilian test is an indirect measure of the tensile
strength. In the test a disc of the material to be tested is
compressed diametrically until the sample fractures or breaks. As
the disc is compressed, a tensional force develops perpendicular
to the direction of the compressive force, within the plane of the
disc. Theoretically, this tensional force will increase until it
reaches the tensile strength of the rock, at which time the rock
will fracture in a plane parallel to the campressional force being
applied. The Brazilian tensile strength (at) is then calculated
by the relation at = 0.636P/Dt, where P is the peak compressive
load at primary fracture, D is the specimen diameter, and t is the
specimen thickness. A thorough discussion of the test procedure
and the theory upon which it is based is found in Mellor and
Hawkes (1971).
A suite of samples from each test group was tested for
Brazilian tensile strength at 25 C dry and after 24 hours
immersion in water. Results of the testing is tabulated in Table
IV. Each group consisted of at least four specimens, with each
core hole represented.


77
TABLE IV
BRAZILIAN TENSILE STRENGTH DATA
tOUP SAMPLE HOLE DEPTH LENGTH DIAMETER
NUMBER NUMBER (FT) (IN) (IN)
(25 DEGREES CENTIGRADE)
A 1 551 85.90 1.115 1.872
A 2 551 90.95 1.027 1.870
A 3 553 83.20 1.190 1.867
A 4 553 83.80 1.274 1.871
A 5 553 85.20 1.112 1.866
A 6 554 98.35 1.143 1.868
A 7 551 90.65 1.113 1.868
A 8 551 90.80 1.053 1.870
A 9 553 83.10 1.167 1.867
A 10 553 85.10 1.104 1.867
A 11 553 86.75 1.234 1.870
A 12 554 96.40 1.068 1.865
A 13 554 98.45 1.186 1.868
B 1 551 98.80 1.247 1.868
B 2 551 99.95 1.227 1.871
B 3 552 54.40 0.996 1.870
B 4 552 54.65 1.145 1.870
B 5 553 94.05 1.335 1.865
B 6 553 95.30 1.267 1.865
B 7 551 98.95 1.171 1.870
B 8 551 101.15 1.293 1.870
B 9 552 55.05 1.090 1.872
B 10 553 93.95 1.323 1.865
B 11 553 95.15 1.235 1.865
C 1 552 88.55 1.184 1.876
c 2 552 91.65 1.050 1.876
c 3 552 95.05 0.993 1.877
c 4 555 28. BO 1.250 1.870
c 5 556 24.90 1.032 1.873
c 6 552 87.95 1.148 1.876
c 7 552 91.85 1.120 1.876
c 8 552 95.15 1.039 1.877
c 9 555 27.40 1.123 1.870
c 10 556 25.90 1.123 1.874
(100 DEGREES CENTIGRADE)
C 1 552 88.95 1.245 1.874
C 2 552 93.15 1.153 1.877
C 3 555 27.30 1.128 1.870
C 4 556 25.80 1.072 1.873
c 5 552 89.05 1.214 1.877
c 6 552 94.25 1.120 1.877
c 7 555 27.20 1.181 1.870
c 8 556 26.80 1.308 1.874
LOAD, BRAZILIAN
WEIGHT DENSITY L/D PRIMARY TENSILE WET/DRY
RATIO FRACTURE STRENGTH
(GRAMS) (PCF) (LB) (PSI)
90.07 111.81 0.596 1310 399 DRY
84.86 114.61 0.549 1440 477 DRY
97.63 114.17 0.637 1570 449 DRY
106.09 115.38 0.681 1820 486 DRY
91.34 114.43 0.596 1400 429 DRY
93.90 114.20 0.612 1310 390 DRY
91.21 113.92 0.596 890 272 WET
86.60 114.08 0.563 720 233 WET
96.45 115.01 0.625 1335 390 WET
90.47 114.03 0.591 1015 313 WET
102.84 115.60 0.660 1170 322 WET
86. B5 113.40 0.573 560 179 WET
97.59 114.38 0.635 980 281 WET
108.01 120.40 0.668 1885 515 DRY
107.63 121.54 0.656 2260 626 DRY
86.60 120.61 0.533 1925 657 DRY
102.40 124.05 0.612 1875 557 DRY
116.14 121.32 0.716 1850 473 DRY
111.65 122.89 0.679 2170 584 DRY
101.46 120.18 0.626 1320 383 WET
114.35 122.67 0.691 2150 566 WET
98.48 125.05 0.582 1475 460 WET
115.30 121.54 0.709 1940 500 WET
108.59 122.62 0.662 1995 551 WET
113.41 132.02 0.631 3860 1105 DRY
100.61 132.06 0.560 3450 1114 DRY
94.72 131.33 0.529 3120 1065 DRY
119.20 132.27 0.668 3535 962 ORY
97.51 130.64 0.551 3340 1099 DRY
109.15 131.04 0.612 2145 633 WET
107.34 132.09 0.597 2245 680 WET
99.35 131.65 0.554 2250 734 WET
106.75 131.85 0.601 1690 512 WET
106.53 131.02 0.599 2035 615 WET
119.19 132.23 0.664 5150 1404 DRY
110.43 131.86 0.614 5220 1534 DRY
107.30 13t.95 0.603 4760 1435 DRY
101.78 131.28 0.572 4140 1311 DRY
116.45 132.06 0.647 2755 769 WET
107.SO 132.15 0.597 2440 738 WET
111.40 130.84 0.632 1950 562 WET
124.69 131.67 0.698 2920 758 WET


78
5.3 Fracture Toughness
5.3.1 Data Compilation
5.3.1.1 Data Tables
Tables V, VI, and VII comprise the physical dimensions and
fracture toughness test results for the three test groups. Within
each test group, specimens are listed according to drill hole and
depth within a given drill hole.
For each fracture toughness test, a peak load (F^^) was
obtained. From this value, the short rod fracture toughness was
calculated by the relationship KgR = (24.0Fmax)/D1*5. A
correction factor was then calculated based upon the variance of
the length of the sample and the variance of the initial crack
length from optimimum values. If the correction factor was less
than 0.99 or greater than 1.01, the KgR value calculated as above
was multiplied by the correction factor to obtain a "corrected"
fracture toughness. These values are listed in the tables.
Lastly, the corrected fracture toughness values have been
converted to SI units for ease in comparison to other studies.
5.3.1.2 Data Tests
ISEM draft guidelines for short rod fracture toughness
testing of core give tolerance ranges for the various dimensions
of prepared specimens. These are summarized as follows (ISFM,
1986, 1988), referring back to Fig. 8:


1
2
3
4
5
6
7
6
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
TABLE V
HOLE
NUMBER
551
551
551
551
551
551
551
551
551
551
551
551
553
553
553
553
553
553
553
553
553
553
553
553
553
553
553
553
554
554
554
554
554
554
554
554
554
554
554
554
DEPTH LENGTH OIAMETER HEIGHT DENSITY l/D L/D NOTCH NOTCH TIP
RATIO SPEC7 SPEC WIDTH POSITION
(FT) (IN) (IN) (GRANS) (PCF) (IN) (IN)
85.65 2.739 1.872 221.42 111.89 1.463 YES 0.0562 0.046 0.90
86.10 2.706 1.870 217.93 111.71 1.447 YES 0.0561 0.045 0.89
86.65 2.678 1.869 216.12 112.06 1.433 YES 0.0561 0.048 0.87
86.85 2.698 1.871 218.54 112.24 1.442 YES 0.0561 0.045 0.88
87.30 2.714 1.870 220.42 112.65 1.451 YES 0.0561 0.046 0.89
87.55 2.720 1.670 220.49 112.44 1.455 YES 0.0561 0.048 0.90
87.60 2.686 1.870 218.17 112.67 1.436 YES 0.0561 0.048 0.86
88.05 2.680 1.873 219.15 113.06 1.431 YES 0.0562 0.047 0.87
89.15 2.732 1.868 224.25 114.10 1.463 YES 0.0560 0.046 0.88
89.40 2.715 1.868 222.10 113.71 1.453 YES 0.0560 0.047 0.90
90.15 2.693 1.869 221.15 114.03 1.441 YES 0.0561 0.048 0.88
91.10 2.688 1.868 221.75 114.68 1.439 YES 0.0560 0.045 0.87
77.95 2.727 1.864 219.98 112.62 1.463 YES 0.0559 0.047 0.90
78.35 2.703 1.871 220.17 112.86 1.445 YES 0.0561 0.045 0.90
78.55 2.683 1.871 217.20 112.17 1.434 YES 0.0561 0.048 0.85
78.80 2.667 1.865 218.63 113.47 1.441 YES 0.0560 0.045 0.88
79.15 2.698 1.864 220.02 113.85 1.447 YES 0.0559 0.047 0.89
79.40 2.693 1.867 221.17 114.29 1.442 YES 0.0560 0.046 0.88
80.15 2.672 1.867 217.74 113.40 1.431 YES 0.0560 0.049 0.82
81.25 2.740 1.875 225.16 113.38 1.461 YES 0.0563 0.047 0.91
81.50 2.714 1.875 224.35 114.05 1.447 YES 0.0563 0.046 0.90
81.75 2.717 1.873 223.06 113.51 1.451 YES 0.0562 0.048 0.89
82.45 2.739 1.867 224.75 114.19 1.467 YES 0.0560 0.047 0.90
82.70 2.704 1.869 221.90 113.95 1.447 YES 0.0561 0.050 0.86
83.75 2.721 1.867 223.90 114.51 1.457 YES 0.0560 0.045 0.91
84.00 2.683 1.867 220.20 114.21 1.437 YES 0.0560 0.046 0.86
84.40 2.689 1.870 222.04 114.54 1.438 YES 0.0561 0.047 0.86
87.35 2.722 1.873 226.37 114.99 1.453 YES 0.0562 0.045 0.89
94.30 2.733 1.860 216.93 111.29 1.469 YES 0.0558 0.052 0.90
94.65 2.724 1.859 216.46 111.53 1.465 YES 0.0558 0.052 0.85
95.25 2.702 1.862 217.11 112.42 1.451 YES 0.0559 0.047 0.85
95.35 2.699 1.864 216.74 112.11 1.448 YES 0.0559 0.049 0.86
95.55 2.701 1.861 217.21 112.63 1.451 YES 0.0558 0.049 0.87
96.80 2.688 1.872 220.07 113.32 1.436 YES 0.0562 0.047 0.87
97.05 2.695 1.870 220.37 113.42 1.441 YES 0.0561 0.050 0.89
97.65 2.704 1.870 220.97 113.35 1.446 YES 0.0561 0.047 0.93
98.85 2.737 1.868 226.24 114.90 1.465 YES 0.0560 0.046 0.90
99.20 2.710 1.868 223.78 114.79 1.451 YES 0.0560 0.045 0.88
99.45 2.705 1.868 223.06 114.63 1.448 YES 0.0560 0.046 0.90
100.25 2.737 1.868 226.55 115.06 1.465 YES 0.0560 0.049 0.90
CORRECTED
FRACTURE CORRECTION FRACTURE
TOUGHNESS FACTOR TOUGHNESS
(PSl*SQRT(IN)I [PSI*SORT(IN)J
0.481 YES 53.9 25 DRY 46.0 431.03 0.9997 431.03
0.476 YES 54.5 200 UET 33.4 313.47 0.9972 313.47
0.465 YES 54.7 100 DRY 45.2 424.56 0.9893 420.02
0.470 YES 54.5 50 UET 35.8 335.72 0.9927 335.72
0.476 YES 54.3 50 DRY 54.0 506.81 0.9967 506.81
0.481 YES 54.4 50 UET 35.6 334.12 1.0012 334.12
0.460 NO 54.2 100 DRY 73.4 688.88 0.9837 677.68
0.464 YES 54.7 50 DRY 59.6 558.02 0.9886 551.68
0.471 YES 53.5 25 UET 33.3 313.03 0.9908 313.03
0.482 YES 54.5 50 UET 38.2 359.09 1.0019 359.09
0.471 YES 54.5 25 UET 34.1 320.30 0.9933 320.30
0.466 YES 54.4 200 UET 38.2 359.09 0.9888 355.08
0.483 YES 54.1 100 DRY 70.2 662.03 1.0016 662.03
0.461 YES 54.8 200 DRY 60.0 562.67 1.0022 562.67
0.454 NO 54.1 25 UET 30.7 287.90 0.9789 281.81
0.472 YES 54.6 200 UET 38.2 359.96 0.9942 359.96
0.477 YES 54.5 50 DRY 60.8 573.38 0.9966 573.38
0.471 YES 54.5 50 DRY 62.2 585.17 0.9936 585.17
0.439 NO 53.5 100 UET 36.2 359.38 0.9652 346.87
0.485 YES 54.3 50 UET 37.2 347.74 1.0041 347.74
0.480 YES 54.7 200 UET 40.4 377.65 1.0009 377.65
0.475 YES 54.3 25 DRY 50.5 472.82 0.9961 472.82
0.482 YES 53.8 100 UET 40.2 378.20 1.0004 378.20
0.460 YES 53.7 25 UET 35.4 332.51 0.9826 326.73
0.487 YES 54.5 100 DRY 58.4 549.42 1.0065 549.42
0.461 YES 54.2 25 DRY 58.0 545.66 0.9843 537.11
0.460 NO 54.2 25 DRY 58.5 549.04 0.9835 540.00
0.475 YES 54.2 50 UET 42.6 398.85 0.9958 398.85
0.484 YES 53.8 25 DRY 47.0 444.67 1.0018 444.67
0.457 NO 52.8 25 UET 25.2 238.61 0.9773 233.20
0.456 NO 53.4 100 UET 29.6 279.60 0.9786 273.63
0.461 YES 53. B 100 UET 30.8 290.46 0.9836 285.71
0.467 YES 53.9 200 DRY 64.0 605.02 0.9889 598.29
0.465 YES 54.5 200 DRY 60.2 564.09 0.9883 557.47
0.476 YES 54.8 200 UET 33.2 311.59 0.9979 311.59
0.497 YES 55.6 50 DRY 59.2 555.61 1.0168 564.96
0.482 YES 53.9 100 DRY 59.6 560.26 1.0004 560.26
0.471 YES 54.1 100 UET 35.0 329.01 0.9923 329.01
0.482 YES 54.7 200 DRY 56.6 532.06 1.0025 532.06
0.482 YES 53.9 200 DRY 63.0 592.22 1.0004 592.22
FRACTURE TOUGHNESS TEST DATA (GROUP A)
azero/D TIP CHEVRON TEMP WET PEAK
SPEC? ANGLE (DEG or LOAD
(DEG) C) DRY (LB)


TABLE VI
FRACTURE TOUGHNESS TEST DATA (GROUP B)
GROUP SAMPLE HOLE DEPTH LENGTH DIAMETER WEIGHT DENSITY
NUMBER NUMBER (FT) (IN) (IN) (GRAMS) (PCF)
B 1 551 98.30 2.717 1.876 235.93 119.68
B 2 551 100.70 2.732 1.872 240.75 121.97
B 3 551 101.30 2.710 1.875 240.49 122.44
B 4 551 101.60 2.717 1.874 240.35 122.16
B 5 551 101.85 2.729 1.873 240.39 121.79
B 6 551 102.10 2.696 1.873 237.45 121.78
B 7 551 102.35 2.686 1.871 236.86 122.19
B 6 551 102.60 2.739 1.870 241.61 122.36
B 9 551 102.80 2.748 1.869 244.07 123.33
B 10 552 52.70 2.722 1.875 242.72 123.03
B 11 552 52.95 2.714 1.875 241.85 122.95
B 12 552 53.20 2.714 1.875 242.30 123.18
B 13 552 53.55 2.714 1.875 242.91 123.49
B 14 552 56.65 2.740 1.872 247.81 125.18
B 15 553 92.60 2.705 1.872 234.50 119.99
B 16 553 92.85 2.720 1.865 235.13 120.55
B 17 553 94.25 2.733 1.866 238.78 121.71
B 18 553 94.60 2.700 1.666 235.59 121.55
B 19 553 94.85 2.722 1.666 238.26 121.94
B 20 553 95.60 2.710 1.867 238.64 122.54
B 21 553 96.10 2.715 1.866 240.40 123.35
B 22 553 96.35 2.714 1.865 240.76 123.71
B 23 553 96.85 2.673 1.869 236.43 122.82
B 24 553 97.10 2.729 1.869 242.62 123.45
B 25 553 97.35 2.734 1.868 240.93 122.50
B 26 553 97.80 2.730 1.869 243.59 123.90
B 27 553 98.10 2.694 1.868 239.93 123.80
B 28 553 98.35 2.738 1.866 244.29 124.29
B 29 553 98.85 2.730 1.867 244.47 124.61
B 30 553 99.30 2.697 1.866 242.61 125.31
B 31 557 13.15 2.727 1.870 235.55 119.81
B 32 557 14.00 2.751 1.873 240.50 120.88
B 33 557 14.25 2.718 1.874 238.34 121.12
B 34 557 14.50 2.721 1.875 239.31 121.34
B 35 557 15.25 2.721 1.875 239.45 121.42
B 36 557 15.50 2.715 1.875 240.31 122.12
B 37 557 15.75 2.732 1.676 241.82 121.99
B 38 557 16.25 2.740 1.875 242.83 122.28
B 39 557 16.55 2.697 1.875 238.44 121.98
L/D L/D NOTCH NOTCH TIP azero/D TIP CHEVRON TEMP
RATIO SPEC? SPEC WIDTH POSITION SPEC? ANGLE (DEG
(IN) (IN) (DEG) C)
1.448 YES 0.0563 0.048 0.91 0.485 YES 54.9 200
1.459 TES 0.0562 0.048 0.93 0.497 YES 54.9 25
1.445 YES 0.0563 0.048 0.90 0.480 TES 54.8 200
1.450 TES 0.0562 0.047 0.91 0.486 TES 54.8 100
1.457 YES 0.0562 0.048 0.91 0.486 YES 54.5 25
1.439 YES 0.0562 0.045 0.86 0.459 NO 54.1 100
1.436 YES 0.0561 0.048 0.87 0.465 YES 54.5 200
1.465 YES 0.0561 0.044 0.68 0.471 YES 53.4 100
1.470 NO 0.0561 0.044 0.89 0.476 TES 53.4 100
1.452 YES 0.0563 0.048 0.92 0.491 YES 55.0 25
1.447 YES 0.0563 0.048 0.93 0.496 YES 55.4 50
1.447 YES 0.0563 0.046 0.90 0.480 YES 54.7 50
1.447 YES 0.0563 0.046 0.90 0.480 YES 54.7 100
1.464 YES 0.0562 0.045 0.91 0.486 YES 54.2 25
1.445 YES 0.0562 0.045 0.90 0.481 YES 54.8 200
1.458 YES 0.0560 0.048 0.90 0.483 YES 54.3 25
1.465 YES 0.0560 0.044 0.88 0.472 YES 53.5 25
1.447 YES 0.0560 0.048 0.89 0.477 YES 54.5 50
1.459 YES 0.0560 0.047 0.90 0.482 YES 54.2 50
1.452 YES 0.0560 0.047 0.89 0.477 YES 54.3 50
1.455 YES 0.0560 0.045 0.90 0.482 YES 54.4 25
1.455 YES 0.0560 0.043 0.85 0.456 NO 53.2 100
1.430 TES 0.0561 0.046 0.66 0.460 YES 54.5 50
1.460 YES 0.0561 0.050 0.88 0.471 YES 53.6 100
1.464 YES 0.0560 0.044 0.92 0.493 YES 54.5 100
1.461 YES 0.0561 0.046 0.94 0.503 NO 55.1 50
1.442 YES 0.0560 0.047 0.89 0.476 YES 54.7 200
1.467 YES 0.0560 0.044 0.92 0.493 YES 54.3 25
1.462 YES 0.0560 0.047 0.90 0.482 YES 54.1 100
1.445 YES 0.0560 0.045 0.88 0.472 YES 54.4 200
1.458 YES 0.0561 0.048 0.92 0.492 YES 54.7 200
1.469 TES 0.0562 0.044 0.92 0.491 YES 54.2 50
1.450 YES 0.0562 0.046 0.91 0.486 YES 54.0 200
1.451 YES 0.0563 0.048 0.93 0.496 YES 55.3 25
1.451 YES 0.0563 0.048 0.91 0.485 YES 54.7 100
1.448 YES 0.0563 0.045 0.91 0.485 YES 54.9 25
1.456 YES 0.0563 0.046 0.94 0.501 NO 55.3 50
1.461 YES 0.0563 0.045 0.92 0.491 YES 54.5 200
1.438 TES 0.0563 0.046 0.89 0.475 YES 54.8 200
CORRECTED CORRECTED
WET PEAK FRACTURE CORRECTION FRACTURE FRACTURE
or LOAD TOUGHNESS FACTOR TOUGHNESS TOUGHNESS
DRY (LB) [PSI*SQRT(IN)J [PSI*SORT(!N)J tkN*(m)**(-1
WET 46.6 437.13 1.0055 437.13 481.28
DRY 61.5 763.68 1.0149 775.06 853.34
WET 59.0 551.52 1.0012 551.52 607.22
DRY 87.2 815.78 1.0058 815.78 898.17
WET 53.4 499.97 1.0052 499.97 550.47
WET 62.0 580.49 0.9827 570.44 628.05
DRY 83.0 778.36 0.9885 769.43 847.14
DRY 99.2 931.02 0.9900 921.70 1014.60
WET 61.2 574.64 0.9945 574.84 632.90
WET 50.0 467.39 1.0102 472.15 519.83
DRY 78.6 734.74 1.0155 746.11 821.47
DRY 81.2 759.04 1.0009 759.04 835.70
WET 55.0 514.13 1.0009 514.13 566.06
DRY 78.5 735.57 1.0046 735.57 809.86
DRY 77.2 723.39 1.0019 723.39 796.45
WET 51.7 487.17 1.0020 487.17 536.38
DRY 80.5 757.95 0.9909 757.95 834.50
DRY 85.2 802.20 0.9982 802.20 883.22
WET 58.2 547.98 1.0017 547.98 603.33
DRY 84.4 794.03 0.9974 794.03 874.23
WET 57.3 539.51 1.0021 539.51 594.00
WET 66.6 627.58 0.9774 613.39 675.34
WET 59.4 557.94 0.9847 549.41 604.90
WET 63.2 593.63 0.9908 593.63 653.58
DRY 115.0 1081.05 1.0105 1092.38 1202.71
WET 62.8 589.87 1.0204 601.88 662.67
WET 60.4 567.78 0.9983 567.78 625.13
DRY 64.5 607.30 1.0105 613.69 675.67
DRY 50.0 470.40 1.0010 470.40 517.91
DRY 97.8 920.84 0.9934 920.84 1013.84
DRY 68.2 640.08 1.0106 646.88 712.22
DRY 63.4 780.86 1.0086 780.86 859.72
WET 47.0 439.70 1.0057 439.70 484.11
WET 44.6 416.91 1.0151 423.20 465.94
DRY 62.4 583.30 1.0054 583.30 642.22
DRY 72.5 677.72 1.0057 677.72 746.16
WET 50.8 474.49 1.0191 483.57 532.41
DRY 74.2 693.61 1.0091 693.61 763.66
WET 54.0 504.78 0.9971 504.78 555.76


TABLE VII
FRACTURE TOUGHNESS TEST DATA (GROUP C)
CORRECTED CORRECTED
GROUP SAMPLE HOLE DEPTH LENGTH DIAMETER WEIGHT DENSITT
NUMBER NUMBER (FT) (IN) (IN) (GRAMS) (PCF)
C 1 552 86.65 2.738 1.678 259.65 130.42
c 2 552 87.70 2.740 1.878 261.41 131.21
c 3 552 88.15 2.724 1.878 263.10 132.84
c 4 552 88.35 2.728 1.878 263.75 132.97
c 5 552 68.75 2.740 1.878 265.93 133.48
c 6 552 89.30 2.751 1.877 265.50 132.87
c 7 552 89.80 2.745 1.875 263.34 132.36
c a 552 90.10 2.721 1.878 259.49 131.16
c 9 552 91.45 2.737 1.078 263.25 132.26
c 10 552 92.05 2.713 1.878 261.04 132.33
c 11 552 92.30 2.711 1.678 261.64 132.73
C 12 552 92.70 2.722 1.878 262.10 132.43
c 13 552 93.40 2.739 1.879 260.81 130.62
c 14 552 94.05 2.723 1.878 262.00 132.33
c 15 552 94.65 2.743 1.880 262.42 131.29
c 16 552 94.90 2.707 1.880 260.96 132.30
c 17 552 95.55 2.686 1.678 256.91 131.54
c 18 552 96.30 2.727 1.875 258.42 130.75
c 19 555 25.15 2.737 1.873 259.58 131.13
c 20 555 25.35 2.728 1.674 258.17 130.71
c 21 555 25.90 2.745 1.871 257.67 130.07
c 22 555 27.80 2.743 1.869 263.17 133.22
c 23 555 28.15 2.705 1.670 260.11 133.38
c 24 555 28.65 2.745 1.870 264.98 133.90
c 25 555 29.05 2.745 1.672 265.96 134.11
c 26 555 29.30 2.721 1.872 263.74 134.16
c 27 555 31.65 2.717 1.872 264.80 134.90
c 28 555 33.65 2.718 1.871 264.76 134.97
c 29 555 33.90 2.712 1.871 262.63 134.18
c 30 555 34.70 2.703 1.870 261.66 134.28
c 31 555 34.15 2.708 1.870 262.82 134.62
c 32 555 35.20 2.722 1.871 264.16 134.48
c 33 555 35.90 2.722 1.869 263.25 134.29
c 34 555 37.65 2.709 1.870 262.12 134.21
c 35 555 40.35 2.700 1.870 262.39 134.60
c 36 556 24.65 2.705 1.875 257.17 131.17
c 37 556 25.65 2.730 1.875 258.54 130.66
c 38 556 26.20 2.710 1.872 257.70 131.62
c 39 556 26.65 2.725 1.672 258.13 131.11
c 40 556 27.10 2.704 1.670 255.69 131.16
L/D L/D NOTCH NOTCH TIP azero/D TIP CHEVRON TEMP
RATIO SPEC? SPEC WIDTH POSITION SPEC? ANGLE (DEG
(IN) (IN) (DEG) C)
1.458 YES 0.0563 0.046 0.91 0.485 YES 54.4 100
1.459 YES 0.0563 0.051 0.93 0.495 YES 54.8 50
1.450 YES 0.0563 0.055 0.89 0.474 YES 54.2 100
1.453 YES 0.0563 0.045 0.93 0.495 YES 55.2 50
1.459 YES 0.0563 0.047 0.90 0.479 YES 54.1 25
1.466 YES 0.0563 0.040 0.93 0.495 YES 54.5 200
1.464 YES 0.0563 0.043 0.92 0.491 YES 54.4 200
1.449 YES 0.0563 0.047 0.92 0.490 YES 55.1 25
1.457 YES 0.0563 0.045 0.92 0.490 YES 54.7 200
1.445 YES 0.0563 0.045 0.90 0.479 YES 54.6 50
1.444 YES 0.0563 0.045 0.90 0.479 YES 54.8 25
1.449 YES 0.0563 0.045 0.93 0.495 YES 55.3 25
1.458 YES 0.0564 0.045 0.90 0.479 YES 54.1 100
1.450 YES 0.0563 0.043 0.92 0.490 YES 55.0 50
1.459 YES 0.0564 0.045 0.92 0.489 YES 54.6 200
1.440 YES 0.0564 0.046 0.90 0.479 YES 55.0 50
1.430 YES 0.0563 0.045 0.86 0.458 NO 54.4 25
1.454 YES 0.0563 0.046 0.92 0.491 YES 54.8 50
1.461 YES 0.0562 0.044 0.91 0.486 YES 54.3 50
1.456 YES 0.0562 0.046 0.90 0.480 YES 54.3 50
1.467 YES 0.0561 0.046 0.91 0.486 YES 54.0 200
1.468 YES 0.0561 0.042 0.90 0.482 YES 53.8 200
1.447 YES 0.0561 0.044 0.87 0.465 YES 54.0 200
1.468 YES 0.0561 0.044 0.88 0.471 YES 53.3 100
1.466 YES 0.0562 0.047 0.89 0.475 YES 53.5 25
1.454 YES 0.0562 0.043 0.88 0.470 YES 53.9 200
1.451 YES 0.0562 0.046 0.90 0.481 YES 54.5 25
1.453 YES 0.0561 0.047 0.88 0.470 YES 54.0 100
1.449 YES 0.0561 0.045 0.90 0.461 YES 54.6 25
1.445 YES 0.0561 0.046 0.67 0.465 YES 54.1 50
1.448 YES 0.0561 0.046 0.90 0.481 YES 54.7 50
1.455 YES 0.0561 0.044 0.90 0.481 YES 54.4 25
1.456 YES 0.0561 0.043 0.90 0.482 YES 54.3 100
1.449 YES 0.0561 0.048 0.66 0.460 NO 53.6 100
1.444 YES 0.0561 0.040 0.93 0.497 YES 55.7 200
1.443 YES 0.0563 0.043 0.88 0.469 YES 54.4 25
1.456 YES 0.0563 0.043 0.90 0.480 YES 54.3 200
1.448 YES 0.0562 0.048 0.91 0.486 YES 54.9 100
1.456 YES 0.0562 0.044 0.90 0.481 YES 54.3 100
1.446 YES 0.0561 0.046 0.87 0.465 YES 54.0 100
WET PEAK FRACTURE CORRECTION FRACTURE FRACTURE
or LOAD TOUGHNESS FACTOR TOUGHNESS TOUGHNESS
DRY (LB) (PSI*$QRT(IN)] (PSI*SQRT(IN)] [kN*(m)**(-1
WET 70.2 654.64 1.0039 654.64 720.76
WET 82.4 768.41 1.0135 778.79 657.44
DRY 144.8 1350.32 0.9949 1350.32 1486.70
DRY 128.8 1201.11 1.0142 1218.18 1341.22
WET 80.2 747.90 0.9988 747.90 823.44
DRY 128.0 1194.61 1.0130 1210.10 1332.32
DRY 107.2 1002.08 1.0087 1002.08 1103.29
WET 71.2 663.97 1.0098 663.97 731.03
DRY 109.6 1022.06 1.0088 1022.06 1125.29
DRY 128.6 1201.11 1.0005 1201.11 1322.42
DRY 102.5 955.85 1.0007 955.85 1052.40
DRY 103.0 960.52 1.0146 974.50 1072.92
DRY 120.2 1120.02 0.9987 1120.02 1233.14
WET 72.2 673.29 1.0097 673.29 741.30
DRY 110.2 1026.02 1.0081 1026.02 1129.65
DRY 123.0 1145.20 1.0006 1145.20 1260.86
WET 74.2 691.95 0.9827 679.96 748.64
WET 73.2 684.26 1.0099 684.26 753.37
DRY 94.4 883.85 1.0046 B83.B5 973.11
DRY 98.0 916.82 1.0002 916.82 1009.42
WET 62.0 581.42 1.0044 581.42 640.15
WET 73.0 685.68 0.9998 685.68 754.93
WET 73.2 687.01 0.9874 678.36 746.67
WET 73.0 685.13 0.9895 677.97 746.44
DRY 114.5 1072.90 0.9943 1072.90 1181.26
WET 81.4 762.74 0.9910 762.74 839.78
DRY 126.5 1185.34 1.0012 1185.34 1305.06
DRY 147.6 13B4.16 0.9914 1384.16 1523.96
DRY 114.5 1073.76 1.0016 1073.76 1182.21
WET 90.8 852.19 0.9875 841.58 926.57
WET 89.6 840.92 1.0020 840.92 925.86
WET 83.6 783.98 1.0010 783.98 863.17
WET 87.6 822.81 1.0013 B22.81 905.92
DRY 142.2 1334.59 0.9822 1310.78 1443.17
DRY 161.0 1511.04 1.0170 1536.79 1692.00
WET 75.6 706.69 0.9917 706.69 778.07
WET 68.0 635.65 0.9999 635.65 699.85
WET 68.2 826.46 1.0065 826.46 909.93
DRY 138.2 1294.97 1.0006 1294.97 1425.76
WET 79.6 747.07 0.9875 737.72 812.23
00


82
Geometry Parameter___________Value______Tolerance
Specimen diameter D (or B) > 10 times grain
size
Specimen length, w 1.45D 0.02 D
Subtended chevron angle, 20 54.6 1.0
Chevron V-top position, a^ 0.48 D 0.02D
Notch width, t < 0.03D or 1 ran, whichever
is greater
Two values, the specimen length and the chevron V-tip
position (a0) were tested as the data tables were developed.
Results are presented as a "YES" or "NO," signifying whether or
not the particular tolerance was met. Actual tolerances of other
parameters, such as notch width, can be surmised by examining the
tables.
5.3.1.3 Data Sorting
To aid in evaluating the data and developing graphs
showing various data relationships, the data tables were sorted
according to the test temperature and the wet or dry condition.
Sorting results in tables in which the data is grouped according
to test sub-groups, which facilitates evaluating to data.
5.3.2 Group Results
5.3.2.1 Group A
For Group A the fracture toughness data are listed by test
temperature in Table VIII. In Figs. 19 through 22, fracture
toughness is plotted against density for each test temperature.


83
DRY
TABLE VIII
GROUP A
FRACTURE TOUGHNESS DATA SUMMARY
(MEAN VALUES)
FRACTURE FRACTURE
TEMP DENSITY TOUGHNESS TOUGHNESS
DEG C pcf psi*sqrt(in) kN*(m)**(-1
25 113.1 485 534
50 113.4 556 612
100 113.8 510 562
200 113.7 569 626
25 113.2 295 325
50 113.4 355 391
100 113.4 323 356
200 113.5 344 379
WET


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Fig. 20. Group A: Plot of fracture
density at 50 C

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DRY TESTS + WET TESTS